26.2: Bacterial Diseases of the Nervous System
- Identify the most common bacteria that can cause infections of the nervous system
- Compare the major characteristics of specific bacterial diseases affecting the nervous system
Bacterial infections that affect the nervous system are serious and can be life-threatening. Fortunately, there are only a few bacterial species commonly associated with neurological infections.
Bacterial Meningitis
Bacterial meningitis is one of the most serious forms of meningitis. Bacteria that cause meningitis often gain access to the CNS through the bloodstream after trauma or as a result of the action of bacterial toxins. Bacteria may also spread from structures in the upper respiratory tract, such as the oropharynx, nasopharynx, sinuses, and middle ear. Patients with head wounds or cochlear implants (an electronic device placed in the inner ear) are also at risk for developing meningitis.
Many of the bacteria that can cause meningitis are commonly found in healthy people. The most common causes of non-neonatal bacterial meningitis are Neisseria meningitidis , Streptococcus pneumoniae , and Haemophilus influenzae . All three of these bacterial pathogens are spread from person to person by respiratory secretions. Each can colonize and cross through the mucous membranes of the oropharynx and nasopharynx, and enter the blood. Once in the blood, these pathogens can disseminate throughout the body and are capable of both establishing an infection and triggering inflammation in any body site, including the meninges (Figure \(\PageIndex{1}\)). Without appropriate systemic antibacterial therapy, the case-fatality rate can be as high as 70%, and 20% of those survivors may be left with irreversible nerve damage or tissue destruction, resulting in hearing loss, neurologic disability, or loss of a limb. Mortality rates are much lower (as low as 15%) in populations where appropriate therapeutic drugs and preventive vaccines are available. 1
A variety of other bacteria, including Listeria monocytogenes and Escherichia coli , are also capable of causing meningitis. These bacteria cause infections of the arachnoid mater and CSF after spreading through the circulation in blood or by spreading from an infection of the sinuses or nasopharynx. Streptococcus agalactiae , commonly found in the microbiota of the vagina and gastrointestinal tract, can also cause bacterial meningitis in newborns after transmission from the mother either before or during birth.
The profound inflammation caused by these microbes can result in early symptoms that include severe headache, fever, confusion, nausea, vomiting, photophobia, and stiff neck. Systemic inflammatory responses associated with some types of bacterial meningitis can lead to hemorrhaging and purpuric lesions on skin, followed by even more severe conditions that include shock, convulsions, coma, and death—in some cases, in the span of just a few hours.
Diagnosis of bacterial meningitis is best confirmed by analysis of CSF obtained by a lumbar puncture. Abnormal levels of polymorphonuclear neutrophils (PMNs) (> 10 PMNs/mm 3 ), glucose (< 45 mg/dL), and protein (> 45 mg/dL) in the CSF are suggestive of bacterial meningitis. 2 Characteristics of specific forms of bacterial meningitis are detailed in the subsections that follow.
Meningococcal Meningitis
Meningococcal meningitis is a serious infection caused by the gram-negative coccus N. meningitidis . In some cases, death can occur within a few hours of the onset of symptoms. Nonfatal cases can result in irreversible nerve damage, resulting in hearing loss and brain damage, or amputation of extremities because of tissue necrosis.
Meningococcal meningitis can infect people of any age, but its prevalence is highest among infants, adolescents, and young adults. 3 Meningococcal meningitis was once the most common cause of meningitis epidemics in human populations. This is still the case in a swath of sub-Saharan Africa known as the meningitis belt, but meningococcal meningitis epidemics have become rare in most other regions, thanks to meningococcal vaccines. However, outbreaks can still occur in communities, schools, colleges, prisons, and other populations where people are in close direct contact.
N. meningitidis has a high affinity for mucosal membranes in the oropharynx and nasopharynx. Contact with respiratory secretions containing N. meningitidis is an effective mode of transmission. The pathogenicity of N. meningitidis is enhanced by virulence factors that contribute to the rapid progression of the disease. These include lipooligosaccharide (LOS) endotoxin, type IV pili for attachment to host tissues, and polysaccharide capsules that help the cells avoid phagocytosis and complement-mediated killing. Additional virulence factors include IgA protease(which breaks down IgA antibodies), the invasion factors Opa, Opc, and porin (which facilitate transcellular entry through the blood-brain barrier), iron-uptake factors (which strip heme units from hemoglobin in host cells and use them for growth), and stress proteins that protect bacteria from reactive oxygen molecules.
A unique sign of meningococcal meningitis is the formation of a petechial rash on the skin or mucous membranes, characterized by tiny, red, flat, hemorrhagic lesions. This rash, which appears soon after disease onset, is a response to LOS endotoxin and adherence virulence factors that disrupt the endothelial cells of capillaries and small veins in the skin. The blood vessel disruption triggers the formation of tiny blood clots, causing blood to leak into the surrounding tissue. As the infection progresses, the levels of virulence factors increase, and the hemorrhagic lesions can increase in size as blood continues to leak into tissues. Lesions larger than 1.0 cm usually occur in patients developing shock, as virulence factors cause increased hemorrhage and clot formation. Sepsis, as a result of systemic damage from meningococcal virulence factors, can lead to rapid multiple organ failure, shock, disseminated intravascular coagulation, and death.
Because meningococcoal meningitis progresses so rapidly, a greater variety of clinical specimens are required for the timely detection of N. meningitidis . Required specimens can include blood, CSF, naso- and oropharyngeal swabs, urethral and endocervical swabs, petechial aspirates, and biopsies. Safety protocols for handling and transport of specimens suspected of containing N. meningitidis should always be followed, since cases of fatal meningococcal disease have occurred in healthcare workers exposed to droplets or aerosols from patient specimens. Prompt presumptive diagnosis of meningococcal meningitis can occur when CSF is directly evaluated by Gram stain, revealing extra- and intracellular gram-negative diplococci with a distinctive coffee-bean microscopic morphology associated with PMNs (Figure \(\PageIndex{2}\)). Identification can also be made directly from CSF using latex agglutination and immunochromatographic rapid diagnostic tests specific for N. meningitidis . Species identification can also be performed using DNA sequence-based typing schemes for hypervariable outer membrane proteins of N. meningitidis , which has replaced sero(sub)typing.
Meningococcal infections can be treated with antibiotic therapy, and third-generation cephalosporins are most often employed. However, because outcomes can be negative even with treatment, preventive vaccination is the best form of treatment. In 2010, countries in Africa’s meningitis belt began using a new serogroup A meningococcal conjugate vaccine. This program has dramatically reduced the number of cases of meningococcal meningitis by conferring individual and herd immunity.
Twelve different capsular serotypes of N. meningitidis are known to exist. Serotypes A, B, C, W, X, and Y are the most prevalent worldwide. The CDC recommends that children between 11–12 years of age be vaccinated with a single dose of a quadrivalent vaccine that protects against serotypes A, C, W, and Y, with a booster at age 16. 4 An additional booster or injections of serogroup B meningococcal vaccine may be given to individuals in high-risk settings (such as epidemic outbreaks on college campuses).
College students living in dorms or communal housing are at increased risk for contracting epidemic meningitis. From 2011 to 2015, there have been at least nine meningococcal outbreaks on college campuses in the United States. These incidents involved a total of 43 students (of whom four died). 5 In spite of rapid diagnosis and aggressive antimicrobial treatment, several of the survivors suffered from amputations or serious neurological problems.
Prophylactic vaccination of first-year college students living in dorms is recommended by the CDC, and insurance companies now cover meningococcal vaccination for students in college dorms. Some colleges have mandated vaccination with meningococcal conjugate vaccine for certain students entering college (Figure \(\PageIndex{3}\)).
Pneumococcal Meningitis
Pneumococcal meningitis is caused by the encapsulated gram-positive bacterium S. pneumoniae (pneumococcus, also called strep pneumo). This organism is commonly found in the microbiota of the pharynx of 30–70% of young children, depending on the sampling method, while S. pneumoniae can be found in fewer than 5% of healthy adults. Although it is often present without disease symptoms, this microbe can cross the blood-brain barrier in susceptible individuals. In some cases, it may also result in septicemia. Since the introduction of the Hib vaccine, S. pneumoniae has become the leading cause of meningitis in humans aged 2 months through adulthood.
S. pneumoniae can be identified in CSF samples using gram-stained specimens, latex agglutination, and immunochromatographic RDT specific for S. pneumoniae . In gram-stained samples, S. pneumoniae appears as gram-positive, lancet-shaped diplococci (Figure \(\PageIndex{4}\)). Identification of S. pneumoniae can also be achieved using cultures of CSF and blood, and at least 93 distinct serotypes can be identified based on the quellung reaction to unique capsular polysaccharides. PCR and RT-PCR assays are also available to confirm identification.
Major virulence factors produced by S. pneumoniae include PI-1 pilin for adherence to host cells (pneumococcal adherence) and virulence factor B (PavB) for attachment to cells of the respiratory tract; choline-binding proteins(cbpA) that bind to epithelial cells and interfere with immune factors IgA and C3; and the cytoplasmic bacterial toxin pneumolysin that triggers an inflammatory response.
With the emergence of drug-resistant strains of S. pneumoniae , pneumococcal meningitis is typically treated with broad-spectrum antibiotics, such as levofloxacin, cefotaxime, penicillin, or other β-lactam antibiotics. The two available pneumococcal vaccines are described in Bacterial Infections of the Respiratory Tract .
Haemophilus influenzae Type b
Meningitis due to H. influenzae serotype b (Hib), an encapsulated pleomorphic gram-negative coccobacilli, is now uncommon in most countries, because of the use of the effective Hib vaccine. Without the use of the Hib vaccine, H. influenzae can be the primary cause of meningitis in children 2 months thru 5 years of age. H. influenzae can be found in the throats of healthy individuals, including infants and young children. By five years of age, most children have developed immunity to this microbe. Infants older than 2 months of age, however, do not produce a sufficient protective antibody response and are susceptible to serious disease. The intracranial pressure caused by this infection leads to a 5% mortality rate and 20% incidence of deafness or brain damage in survivors. 6
H. influenzae produces at least 16 different virulence factors, including LOS, which triggers inflammation, and Haemophilus adhesion and penetration factor (Hap), which aids in attachment and invasion into respiratory epithelial cells. The bacterium also has a polysaccharide capsule that helps it avoid phagocytosis, as well as factors such as IgA1 protease and P2 protein that allow it to evade antibodies secreted from mucous membranes. In addition, factors such as hemoglobin-binding protein (Hgp) and transferrin-binding protein (Tbp) acquire iron from hemoglobin and transferrin, respectively, for bacterial growth.
Preliminary diagnosis of H. influenzae infections can be made by direct PCR and a smear of CSF. Stained smears will reveal intracellular and extracellular PMNs with small, pleomorphic, gram-negative coccobacilli or filamentous forms that are characteristic of H. influenzae . Initial confirmation of this genus can be based on its fastidious growth on chocolate agar. Identification is confirmed with requirements for exogenous biochemical growth cofactors NAD and heme (by MALDI-TOF), latex agglutination, and RT-PCR.
Meningitis caused by H. influenzae is usually treated with doxycycline, fluoroquinolones, second- and third-generation cephalosporins, and carbapenems. The best means of preventing H. influenza infection is with the use of the Hib polysaccharide conjugate vaccine. It is recommended that all children receive this vaccine at 2, 4, and 6 months of age, with a final booster dose at 12 to 15 months of age. 7
Neonatal Meningitis
S. agalactiae , Group B streptococcus (GBS), is an encapsulated gram-positive bacterium that is the most common cause of neonatal meningitis, a term that refers to meningitis occurring in babies up to 3 months of age. 8 S. agalactiae can also cause meningitis in people of all ages and can be found in the urogenital and gastrointestinal microbiota of about 10–30% of humans.
Neonatal infection occurs as either early onset or late-onset disease. Early onset disease is defined as occurring in infants up to 7 days old. The infant initially becomes infected by S. agalactiae during childbirth, when the bacteria may be transferred from the mother’s vagina. Incidence of early onset neonatal meningitis can be greatly reduced by giving intravenous antibiotics to the mother during labor.
Late-onset neonatal meningitis occurs in infants between 1 week and 3 months of age. Infants born to mothers with S. agalactiae in the urogenital tract have a higher risk of late-onset menigitis, but late-onset infections can be transmitted from sources other than the mother; often, the source of infection is unknown. Infants who are born prematurely (before 37 weeks of pregnancy) or to mothers who develop a fever also have a greater risk of contracting late-onset neonatal meningitis.
Signs and symptoms of early onset disease include temperature instability, apnea (cessation of breathing), bradycardia(slow heart rate), hypotension, difficulty feeding, irritability, and limpness. When asleep, the baby may be difficult to wake up. Symptoms of late-onset disease are more likely to include seizures, bulging fontanel (soft spot), stiff neck, hemiparesis (weakness on one side of the body), and opisthotonos (rigid body with arched back and head thrown backward).
S. agalactiae produces at least 12 virulence factors that include FbsA that attaches to host cell surface proteins, PI-1 pilithat promotes the invasion of human endothelial cells, a polysaccharide capsule that prevents the activation of the alternative complement pathway and inhibits phagocytosis, and the toxin CAMP factor, which forms pores in host cell membranes and binds to IgG and IgM antibodies.
Diagnosis of neonatal meningitis is often, but not uniformly, confirmed by positive results from cultures of CSF or blood. Tests include routine culture, antigen detection by enzyme immunoassay, serotyping of different capsule types, PCR, and RT-PCR. It is typically treated with β-lactam antibiotics such as intravenous penicillin or ampicillin plus gentamicin. Even with treatment, roughly 10% mortality is seen in infected neonates. 9
- Which groups are most vulnerable to each of the bacterial meningitis diseases?
- For which of the bacterial meningitis diseases are there vaccines presently available?
- Which organism can cause epidemic meningitis?
Clostridium-Associated Diseases
Species in the genus Clostridium are gram-positive, endospore-forming rods that are obligate anaerobes. Endospores of Clostridium spp. are widespread in nature, commonly found in soil, water, feces, sewage, and marine sediments. Clostridium spp. produce more types of protein exotoxins than any other bacterial genus, including two exotoxins with protease activity that are the most potent known biological toxins: botulinum neurotoxin (BoNT) and tetanus neurotoxin (TeNT). These two toxins have lethal doses of 0.2–10 ng per kg body weight.
BoNT can be produced by unique strains of C. butyricum , and C. baratii ; however, it is primarily associated with C. botulinum and the condition of botulism. TeNT, which causes tetanus, is only produced by C. tetani . These powerful neural exotoxins are the primary virulence factors for these pathogens. The mode of action for these toxins was described in Virulence Factors of Bacterial and Viral Pathogens and illustrated in Figure 15.3.7 .
Diagnosis of tetanus or botulism typically involves bioassays that detect the presence of BoNT and TeNT in fecal specimens, blood (serum), or suspect foods. In addition, both C. botulinum and C. tetani can be isolated and cultured using commercially available media for anaerobes. ELISA and RT-PCR tests are also available.
Tetanus
Tetanus is a noncommunicable disease characterized by uncontrollable muscle spasms (contractions) caused by the action of TeNT. It generally occurs when C. tetani infects a wound and produces TeNT, which rapidly binds to neural tissue, resulting in an intoxication (poisoning) of neurons. Depending on the site and extent of infection, cases of tetanus can be described as localized, cephalic, or generalized. Generalized tetanus that occurs in a newborn is called neonatal tetanus.
Localized tetanus occurs when TeNT only affects the muscle groups close to the injury site. There is no CNS involvement, and the symptoms are usually mild, with localized muscle spasms caused by a dysfunction in the surrounding neurons. Individuals with partial immunity—especially previously vaccinated individuals who neglect to get the recommended booster shots—are most likely to develop localized tetanus as a result of C. tetani infecting a puncture wound.
Cephalic tetanus is a rare, localized form of tetanus generally associated with wounds on the head or face. In rare cases, it has occurred in cases of otitis media (middle ear infection). Cephalic tetanus often results in patients seeing double images, because of the spasms affecting the muscles that control eye movement.
Both localized and cephalic tetanus may progress to generalized tetanus—a much more serious condition—if TeNT is able to spread further into body tissues. In generalized tetanus, TeNT enters neurons of the PNS. From there, TeNT travels from the site of the wound, usually on an extremity of the body, retrograde (back up) to inhibitory neurons in the CNS. There, it prevents the release of gamma aminobutyric acid (GABA), the neurotransmitter responsible for muscle relaxation. The resulting muscle spasms often first occur in the jaw muscles, leading to the characteristic symptom of lockjaw (inability to open the mouth). As the toxin progressively continues to block neurotransmitter release, other muscles become involved, resulting in uncontrollable, sudden muscle spasms that are powerful enough to cause tendons to rupture and bones to fracture. Spasms in the muscles in the neck, back, and legs may cause the body to form a rigid, stiff arch, a posture called opisthotonos (Figure \(\PageIndex{5}\)). Spasms in the larynx, diaphragm, and muscles of the chest restrict the patient’s ability to swallow and breathe, eventually leading to death by asphyxiation (insufficient supply of oxygen).
Neonatal tetanus typically occurs when the stump of the umbilical cord is contaminated with spores of C. tetani after delivery. Although this condition is rare in the United States, neonatal tetanus is a major cause of infant mortality in countries that lack maternal immunization for tetanus and where birth often occurs in unsanitary conditions. At the end of the first week of life, infected infants become irritable, feed poorly, and develop rigidity with spasms. Neonatal tetanus has a very poor prognosis with a mortality rate of 70%–100%. 10
Treatment for patients with tetanus includes assisted breathing through the use of a ventilator, wound debridement, fluid balance, and antibiotic therapy with metronidazole or penicillin to halt the growth of C. tetani . In addition, patients are treated with TeNT antitoxin, preferably in the form of human immunoglobulin to neutralize nonfixed toxin and benzodiazepines to enhance the effect of GABA for muscle relaxation and anxiety.
A tetanus toxoid (TT) vaccine is available for protection and prevention of tetanus. It is the T component of vaccines such as DTaP, Tdap, and Td. The CDC recommends children receive doses of the DTaP vaccine at 2, 4, 6, and 15–18 months of age and another at 4–6 years of age. One dose of Td is recommended for adolescents and adults as a TT booster every 10 years. 11
Botulism
Botulism is a rare but frequently fatal illness caused by intoxication by BoNT. It can occur either as the result of an infection by C. botulinum , in which case the bacteria produce BoNT in vivo , or as the result of a direct introduction of BoNT into tissues.
Infection and production of BoNT in vivo can result in wound botulism, infant botulism, and adult intestinal toxemia. Wound botulism typically occurs when C. botulinum is introduced directly into a wound after a traumatic injury, deep puncture wound, or injection site. Infant botulism, which occurs in infants younger than 1 year of age, and adult intestinal toxemia, which occurs in immunocompromised adults, results from ingesting C. botulinum endospores in food. The endospores germinate in the body, resulting in the production of BoNT in the intestinal tract.
Intoxications occur when BoNT is produced outside the body and then introduced directly into the body through food (foodborne botulism), air (inhalation botulism), or a clinical procedure (iatrogenic botulism). Foodborne botulism, the most common of these forms, occurs when BoNT is produced in contaminated food and then ingested along with the food (recall Case in Point: A Streak of Bad Potluck ). Inhalation botulism is rare because BoNT is unstable as an aerosol and does not occur in nature; however, it can be produced in the laboratory and was used (unsuccessfully) as a bioweapon by terrorists in Japan in the 1990s. A few cases of accidental inhalation botulism have also occurred. Iatrogenic botulism is also rare; it is associated with injections of BoNT used for cosmetic purposes (see Micro Connections: Medicinal Uses of Botulinum Toxin ).
When BoNT enters the bloodstream in the gastrointestinal tract, wound, or lungs, it is transferred to the neuromuscular junctions of motor neurons where it binds irreversibly to presynaptic membranes and prevents the release of acetylcholine from the presynaptic terminal of motor neurons into the neuromuscular junction. The consequence of preventing acetylcholine release is the loss of muscle activity, leading to muscle relaxation and eventually paralysis.
If BoNT is absorbed through the gastrointestinal tract, early symptoms of botulism include blurred vision, drooping eyelids, difficulty swallowing, abdominal cramps, nausea, vomiting, constipation, or possibly diarrhea. This is followed by progressive flaccid paralysis, a gradual weakening and loss of control over the muscles. A patient’s experience can be particularly terrifying, because hearing remains normal, consciousness is not lost, and he or she is fully aware of the progression of his or her condition. In infants, notable signs of botulism include weak cry, decreased ability to suckle, and hypotonia (limpness of head or body). Eventually, botulism ends in death from respiratory failure caused by the progressive paralysis of the muscles of the upper airway, diaphragm, and chest.
Botulism is treated with an antitoxin specific for BoNT. If administered in time, the antitoxin stops the progression of paralysis but does not reverse it. Once the antitoxin has been administered, the patient will slowly regain neurological function, but this may take several weeks or months, depending on the severity of the case. During recovery, patients generally must remain hospitalized and receive breathing assistance through a ventilator.
- How frequently should the tetanus vaccination be updated in adults?
- What are the most common causes of botulism?
- Why is botulism not treated with an antibiotic?
Although it is the most toxic biological material known to man, botulinum toxin is often intentionally injected into people to treat other conditions. Type A botulinum toxin is used cosmetically to reduce wrinkles. The injection of minute quantities of this toxin into the face causes the relaxation of facial muscles, thereby giving the skin a smoother appearance. Eyelid twitching and crossed eyes can also be treated with botulinum toxin injections. Other uses of this toxin include the treatment of hyperhidrosis (excessive sweating). In fact, botulinum toxin can be used to moderate the effects of several other apparently nonmicrobial diseases involving inappropriate nerve function. Such diseases include cerebral palsy, multiple sclerosis, and Parkinson’s disease. Each of these diseases is characterized by a loss of control over muscle contractions; treatment with botulinum toxin serves to relax contracted muscles.
Listeriosis
Listeria monocytogenes is a nonencapsulated, nonsporulating, gram-positive rod and a foodborne pathogen that causes listeriosis. At-risk groups include pregnant women, neonates, the elderly, and the immunocompromised (recall the Clinical Focus case studies in Microbial Growth and Microbial Mechanisms of Pathogenicity ). Listeriosis leads to meningitis in about 20% of cases, particularly neonates and patients over the age of 60. The CDC identifies listeriosis as the third leading cause of death due to foodborne illness, with overall mortality rates reaching 16%. 12 In pregnant women, listeriosis can cause also cause spontaneous abortion in pregnant women because of the pathogen’s unique ability to cross the placenta.
L. monocytogenes is generally introduced into food items by contamination with soil or animal manure used as fertilizer. Foods commonly associated with listeriosis include fresh fruits and vegetables, frozen vegetables, processed meats, soft cheeses, and raw milk. 13 Unlike most other foodborne pathogens, Listeria is able to grow at temperatures between 0 °C and 50 °C, and can therefore continue to grow, even in refrigerated foods.
Ingestion of contaminated food leads initially to infection of the gastrointestinal tract. However, L. monocytogenes produces several unique virulence factors that allow it to cross the intestinal barrier and spread to other body systems. Surface proteins called internalins (InlA and InlB) help L. monocytogenes invade nonphagocytic cells and tissues, penetrating the intestinal wall and becoming disseminating through the circulatory and lymphatic systems. Internalins also enable L. monocytogenes to breach other important barriers, including the blood-brain barrier and the placenta. Within tissues, L. monocytogenes uses other proteins called listeriolysin O and ActA to facilitate intercellular movement, allowing the infection to spread from cell to cell (Figure \(\PageIndex{6}\)).
L. monocytogenes is usually identified by cultivation of samples from a normally sterile site (e.g., blood or CSF). Recovery of viable organisms can be enhanced using cold enrichment by incubating samples in a broth at 4 °C for a week or more. Distinguishing types and subtypes of L. monocytogenes —an important step for diagnosis and epidemiology—is typically done using pulsed-field gel electrophoresis. Identification can also be achieved using chemiluminescence DNA probe assays and MALDI-TOF.
Treatment for listeriosis involves antibiotic therapy, most commonly with ampicillin and gentamicin. There is no vaccine available.
How does Listeria enter the nervous system?
Hansen’s Disease (Leprosy)
Hansen’s disease (also known as leprosy) is caused by a long, thin, filamentous rod-shaped bacterium Mycobacterium leprae , an obligate intracellular pathogen. M. leprae is classified as gram-positive bacteria, but it is best visualized microscopically with an acid-fast stain and is generally referred to as an acid-fast bacterium. Hansen’s disease affects the PNS, leading to permanent damage and loss of appendages or other body parts.
Hansen’s disease is communicable but not highly contagious; approximately 95% of the human population cannot be easily infected because they have a natural immunity to M. leprae . Person-to-person transmission occurs by inhalation into nasal mucosa or prolonged and repeated contact with infected skin. Armadillos, one of only five mammals susceptible to Hansen’s disease, have also been implicated in transmission of some cases. 14
In the human body, M. leprae grows best at the cooler temperatures found in peripheral tissues like the nose, toes, fingers, and ears. Some of the virulence factors that contribute to M. leprae ’s pathogenicity are located on the capsule and cell wall of the bacterium. These virulence factors enable it to bind to and invade Schwann cells, resulting in progressive demyelination that gradually destroys neurons of the PNS. The loss of neuronal function leads to hypoesthesia (numbness) in infected lesions. M. leprae is readily phagocytized by macrophages but is able to survive within macrophages in part by neutralizing reactive oxygen species produced in the oxidative burst of the phagolysosome. Like L. monocytogenes , M. leprae also can move directly between macrophages to avoid clearance by immune factors.
The extent of the disease is related to the immune response of the patient. Initial symptoms may not appear for as long as 2 to 5 years after infection. These often begin with small, blanched, numb areas of the skin. In most individuals, these will resolve spontaneously, but some cases may progress to a more serious form of the disease. Tuberculoid (paucibacillary) Hansen’s disease is marked by the presence of relatively few (three or less) flat, blanched skin lesions with small nodules at the edges and few bacteria present in the lesion. Although these lesions can persist for years or decades, the bacteria are held in check by an effective immune response including cell-mediated cytotoxicity. Individuals who are unable to contain the infection may later develop lepromatous (multibacillary) Hansen’s disease. This is a progressive form of the disease characterized by nodules filled with acid-fast bacilli and macrophages. Impaired function of infected Schwann cells leads to peripheral nerve damage, resulting in sensory loss that leads to ulcers, deformities, and fractures. Damage to the ulnar nerve (in the wrist) by M. leprae is one of the most common causes of crippling of the hand. In some cases, chronic tissue damage can ultimately lead to loss of fingers or toes. When mucosal tissues are also involved, disfiguring lesions of the nose and face can also occur (Figure \(\PageIndex{7}\)).
Hansen’s disease is diagnosed on the basis of clinical signs and symptoms of the disease, and confirmed by the presence of acid-fast bacilli on skin smears or in skin biopsy specimens (Figure \(\PageIndex{7}\)). M. leprae does not grow in vitro on any known laboratory media, but it can be identified by culturing in vivo in the footpads of laboratory mice or armadillos. Where needed, PCR and genotyping of M. leprae DNA in infected human tissue may be performed for diagnosis and epidemiology.
Hansen’s disease responds well to treatment and, if diagnosed and treated early, does not cause disability. In the United States, most patients with Hansen’s disease are treated in ambulatory care clinics in major cities by the National Hansen’s Disease program, the only institution in the United States exclusively devoted to Hansen’s disease. Since 1995, WHO has made multidrug therapy for Hansen’s disease available free of charge to all patients worldwide. As a result, global prevalence of Hansen’s disease has declined from about 5.2 million cases in 1985 to roughly 176,000 in 2014. 15 Multidrug therapy consists of dapsone and rifampicin for all patients and a third drug, clofazimin, for patients with multibacillary disease.
Currently, there is no universally accepted vaccine for Hansen’s disease. India and Brazil use a tuberculosis vaccineagainst Hansen’s disease because both diseases are caused by species of Mycobacterium . The effectiveness of this method is questionable, however, since it appears that the vaccine works in some populations but not in others.
- What prevents the progression from tuberculoid to lepromatus leprosy?
- Why does Hansen’s disease typically affect the nerves of the extremities?
Disfiguring, deadly diseases like leprosy have historically been stigmatized in many cultures. Before leprosy was understood, victims were often isolated in leper colonies, a practice mentioned frequently in ancient texts, including the Bible. But leper colonies are not just an artifact of the ancient world. In Hawaii, a leper colony established in the late nineteenth century persisted until the mid-twentieth century, its residents forced to live in deplorable conditions. 16 Although leprosy is a communicable disease, it is not considered contagious (easily communicable), and it certainly does not pose enough of a threat to justify the permanent isolation of its victims. Today, we reserve the practices of isolation and quarantine to patients with more dangerous diseases, such as Ebola or multiple-drug-resistant bacteria like Mycobacterium tuberculosis and Staphylococcus aureus . The ethical argument for this practice is that isolating infected patients is necessary to prevent the transmission and spread of highly contagious diseases—even when it goes against the wishes of the patient.
Of course, it is much easier to justify the practice of temporary, clinical quarantining than permanent social segregation, as occurred in leper colonies. In the 1980s, there were calls by some groups to establish camps for people infected with AIDS. Although this idea was never actually implemented, it begs the question—where do we draw the line? Are permanent isolation camps or colonies ever medically or socially justifiable? Suppose there were an outbreak of a fatal, contagious disease for which there is no treatment. Would it be justifiable to impose social isolation on those afflicted with the disease? How would we balance the rights of the infected with the risk they pose to others? To what extent should society expect individuals to put their own health at risk for the sake of treating others humanely?
Despite the formidable defenses protecting the nervous system, a number of bacterial pathogens are known to cause serious infections of the CNS or PNS. Unfortunately, these infections are often serious and life threatening. Figure \(\PageIndex{8}\) summarizes some important infections of the nervous system.
Key Concepts and Summary
- Bacterial meningitis can be caused by several species of encapsulated bacteria, including Haemophilus influenzae , Neisseria meningitidis , Streptococcus pneumoniae , and Streptococcus agalactiae (group B streptococci). H. influenzae affects primarily young children and neonates, N. meningitidis is the only communicable pathogen and mostly affects children and young adults, S. pneumoniae affects mostly young children, and S. agalactiae affects newborns during or shortly after birth.
- Symptoms of bacterial meningitis include fever, neck stiffness, headache, confusion, convulsions, coma, and death.
- Diagnosis of bacterial meningitis is made through observations and culture of organisms in CSF. Bacterial meningitis is treated with antibiotics. H. influenzae and N. meningitidis have vaccines available.
- Clostridium species cause neurological diseases, including botulism and tetanus , by producing potent neurotoxins that interfere with neurotransmitter release. The PNS is typically affected. Treatment of Clostridium infection is effective only through early diagnosis with administration of antibiotics to control the infection and antitoxins to neutralize the endotoxin before they enter cells.
- Listeria monocytogenes is a foodborne pathogen that can infect the CNS, causing meningitis. The infection can be spread through the placenta to a fetus. Diagnosis is through culture of blood or CSF. Treatment is with antibiotics and there is no vaccine.
- Hansen’s disease ( leprosy ) is caused by the intracellular parasite Mycobacterium leprae . Infections cause demylenation of neurons, resulting in decreased sensation in peripheral appendages and body sites. Treatment is with multi-drug antibiotic therapy, and there is no universally recognized vaccine.
Footnotes
- 1 Thigpen, Michael C., Cynthia G. Whitney, Nancy E. Messonnier, Elizabeth R. Zell, Ruth Lynfield, James L. Hadler, Lee H. Harrison et al., “Bacterial Meningitis in the United States, 1998–2007,” New England Journal of Medicine 364, no. 21 (2011): 2016-25.
- 2 Popovic, T., et al. World Health Organization, “Laboratory Manual for the Diagnosis of Meningitis Caused by Neisseria meningitidis , Streptococcus pneumoniae , and Haemophilus influenza ,” 1999.
- 3 US Centers for Disease Control and Prevention, “Meningococcal Disease,” August 5, 2015. Accessed June 28, 2015. www.cdc.gov/meningococcal/sur...nce/index.html.
- 4 US Centers for Disease Control and Prevention, “Recommended Immunization Schedule for Persons Aged 0 Through 18 Years, United States, 2016,” February 1, 2016. Accessed on June 28, 2016. www.cdc.gov/vaccines/schedule...dolescent.html.
- 5 National Meningitis Association, “Serogroup B Meningococcal Disease Outbreaks on U.S. College Campuses,” 2016. Accessed June 28, 2016. http://www.nmaus.org/disease-prevent...ase/outbreaks/ .
- 6 United States Department of Health and Human Services, “Hib (Haemophilus Influenzae Type B),” Accessed June 28, 2016. http://www.vaccines.gov/diseases/hib/# .
- 7 US Centers for Disease Control and Prevention, “Meningococcal Disease, Disease Trends,” 2015. Accessed September 13, 2016. www.cdc.gov/meningococcal/sur...nce/index.html.
- 8 Thigpen, Michael C., Cynthia G. Whitney, Nancy E. Messonnier, Elizabeth R. Zell, Ruth Lynfield, James L. Hadler, Lee H. Harrison et al., “Bacterial Meningitis in the United States, 1998–2007,” New England Journal of Medicine 364, no. 21 (2011): 2016-25.
- 9 Thigpen, Michael C., Cynthia G. Whitney, Nancy E. Messonnier, Elizabeth R. Zell, Ruth Lynfield, James L. Hadler, Lee H. Harrison et al., “Bacterial Meningitis in the United States, 1998–2007,” New England Journal of Medicine 364, no. 21 (2011): 2016-25; Heath, Paul T., Gail Balfour, Abbie M. Weisner, Androulla Efstratiou, Theresa L. Lamagni, Helen Tighe, Liam AF O’Connell et al., “Group B Streptococcal Disease in UK and Irish Infants Younger than 90 Days,” The Lancet 363, no. 9405 (2004): 292-4.
- 10 UNFPA, UNICEF WHO, “Maternal and Neonatal Tetanus Elimination by 2005,” 2000. www.unicef.org/immunization/f...tegy_paper.pdf.
- 11 US Centers for Disease Control and Prevention, “Tetanus Vaccination,” 2013. Accessed June 29, 2016. http://www.cdc.gov/tetanus/vaccination.html .
- 12 Scallan, Elaine, Robert M. Hoekstra, Frederick J. Angulo, Robert V. Tauxe, Marc-Alain Widdowson, Sharon L. Roy, Jeffery L. Jones, and Patricia M. Griffin, “Foodborne Illness Acquired in the United States—Major Pathogens,” Emerging Infectious Diseases 17, no. 1 (2011): 7-15.
- 13 US Centers for Disease Control and Prevention, “ Listeria Outbreaks,” 2016. Accessed June 29, 2016. https://www.cdc.gov/listeria/outbreaks/index.html .
- 14 Sharma, Rahul, Pushpendra Singh, W. J. Loughry, J. Mitchell Lockhart, W. Barry Inman, Malcolm S. Duthie, Maria T. Pena et al., “Zoonotic Leprosy in the Southeastern United States,” Emerging Infectious Diseases 21, no. 12 (2015): 2127-34.
- 15 World Health Organization, “Leprosy Fact Sheet,” 2016. Accessed September 13, 2016. http://www.who.int/mediacentre/factsheets/fs101/en/ .
- 16 National Park Service, “A Brief History of Kalaupapa,” Accessed February 2, 2016. www.nps.gov/kala/learn/histor...-kalaupapa.htm.
Contributor
-
Nina Parker, (Shenandoah University), Mark Schneegurt (Wichita State University), Anh-Hue Thi Tu (Georgia Southwestern State University), Philip Lister (Central New Mexico Community College), and Brian M. Forster (Saint Joseph’s University) with many contributing authors. Original content via Openstax (CC BY 4.0; Access for free at https://openstax.org/books/microbiology/pages/1-introduction )


14.2: Flowchart kinematics
Go to 18: determine forces and moments from \(\overrightarrow{\boldsymbol{a}}\) and \(\overrightarrow{\boldsymbol{\alpha}}\)
- This flowchart shows the strategy for dealing with kinematics problems.
- First determine if we deal with a rigid body or point mass, since the kinematics of point masses is significantly simpler.
- Kinematics translation: the goal is to determine position \(\overrightarrow{\boldsymbol{r}}\), velocity \(\overrightarrow{\boldsymbol{v}}\) and acceleration \(\overrightarrow{\boldsymbol{a}}\) if only one of the three is known. This is done by solving the ODE, e.g. by differentiation and integration over time \(t\), or along the path \(s\) or angle \(\phi\) coordinate (see Table 5.1). In 3D we have derived equations to differentiate along Cartesian, natural or cylindrical coordinates (
- Rotating coordinate systems: the goal is to determine \(\overrightarrow{\boldsymbol{v}}_{B}, \overrightarrow{\boldsymbol{a}}_{B}\) of point \(B\) in an IRF if \(\overrightarrow{\boldsymbol{v}}_{B}^{\prime}\) and \(\overrightarrow{\boldsymbol{a}}_{B}^{\prime}\) are known in a CS that rotates with angular velocity \(\overrightarrow{\boldsymbol{\Omega}}\), or vice versa (see Sec. 9.7).
- Rotating rigid bodies: the goal is to determine \(\overrightarrow{\boldsymbol{v}}_{B}, \overrightarrow{\boldsymbol{a}}_{B}\) of a point \(B\) that is fixed on a rigid body if \(\overrightarrow{\boldsymbol{\omega}}\) and \(\overrightarrow{\boldsymbol{\alpha}}\) are known or vice versa. Translation of a point is dealt with similar as in step 13. The kinematic equations for rotation of rigid body are discussed in Ch. 9. In particular the instantaneous centre of rotation (IC, see Sec. 9.5.1) can facilitate determination of velocities.
- The kinematic equations are determined using steps 13-15.
- Finally the motion \(\overrightarrow{\boldsymbol{r}}(t), \overrightarrow{\boldsymbol{v}}, \overrightarrow{\boldsymbol{a}}, \overrightarrow{\boldsymbol{\omega}}, \overrightarrow{\boldsymbol{\alpha}}\) is determined by solving the kinematic and constraint (differential) equations. In case one needs to determine forces: go to step 18 to achieve this with kinetics.


22.9: For Further Exploration
Articles
Balick, B. & Frank, A. “The Extraordinary Deaths of Ordinary Stars.” Scientific American (July 2004): 50. About planetary nebulae, the last gasps of low-mass stars, and the future of our own Sun.
Djorgovsky, G. “The Dynamic Lives of Globular Clusters.” Sky & Telescope (October 1998): 38. Cluster evolution and blue straggler stars.
Frank, A. “Angry Giants of the Universe.” Astronomy (October 1997): 32. On luminous blue variables like Eta Carinae.
Garlick, M. “The Fate of the Earth.” Sky & Telescope (October 2002): 30. What will happen when our Sun becomes a red giant.
Harris, W. & Webb, J. “Life Inside a Globular Cluster.” Astronomy (July 2014): 18. What would night sky be like there?
Iben, I. & Tutokov, A. “The Lives of the Stars: From Birth to Death and Beyond.” Sky & Telescope (December 1997): 36.
Kaler, J. “The Largest Stars in the Galaxy.” Astronomy (October 1990): 30. On red supergiants.
Kalirai, J. “New Light on Our Sun’s Fate.” Astronomy (February 2014): 44. What will happen to stars like our Sun between the main sequence and the white dwarf stages.
Kwok, S. “What Is the Real Shape of the Ring Nebula?” Sky & Telescope (July 2000): 33. On seeing planetary nebulae from different angles.
Kwok, S. “Stellar Metamorphosis.” Sky & Telescope (October 1998): 30. How planetary nebulae form.
Stahler, S. “The Inner Life of Star Clusters.” Scientific American (March 2013): 44–49. How all stars are born in clusters, but different clusters evolve differently.
Subinsky, R. “All About 47 Tucanae.” Astronomy (September 2014): 66. What we know about this globular cluster and how to see it.
Websites
Encylopedia Britannica Article on Star Clusters: http://www.britannica.com/topic/star-cluster . Written by astronomer Helen Sawyer Hogg-Priestley.
Hubble Image Gallery: Planetary Nebulae: Go to https://www.spacetelescope.org/images/ and in the search box enter "planetary nebulae". See also a similar gallery from NOIRLab: https://noirlab.edu/public/images/ . (Again, enter "planetary nebulae" in the search box.)
"Hubble Image Gallery: Star Clusters: Go to https://www.spacetelescope.org/images/ and in the search box enter "star clusters". (See also a similar European Southern Observatory Gallery at: https://www.eso.org/public/images/archive/category/starclusters/ ).
Measuring the Age of a Star Cluster: https://www.e-education.psu.edu/astro801/content/l7_p6.html . From Penn State.
Videos
Life Cycle of Stars: https://www.youtube.com/watch?v=PM9CQDlQI0A . Short summary of stellar evolution from the Institute of Physics in Great Britain, with astronomer Tim O’Brien (4:58).
Missions Take an Unparalleled Look into Superstar Eta Carinae: https://www.youtube.com/watch?v=0rJQi6oaZf0 . NASA Goddard video about observations in 2014 and what we know about the pair of stars in this complicated system (4:00).
Star Clusters: Open and Globular Clusters: https://www.youtube.com/watch?v=rGPRLxrYbYA . Three Short Hubblecast Videos from 2007–2008 on discoveries involving star clusters (12:24).
Tour of Planetary Nebula NGC 5189: https://www.youtube.com/watch?v=1D2cwiZld0o . Brief Hubblecast episode with Joe Liske, explaining planetary nebulae in general and one example in particular (5:22).


8: Weather Systems
By the end of the chapter you should be able to:
- Describe the conditions favorable for an air mass source region.
- Describe the characteristics of, and locate the source region for, cP, mP, mT, cT, cA, cAA mE air masses.
- Explain how air masses are modified when they leave their source region.
- Describe the characteristics of fronts.
- Identify cold, warm, stationary and occluded fronts from a weather map.
- Interpret weather conditions from weather maps symbols.
- Describe the polar front theory of cyclogenesis.
- Draw profile views of cold, warm and occluded fronts.
- Explain the relationship between jet streams and surface cyclones.
- Describe the weather changes that occur as a midlatitude cyclone passes.
- Compare and contrast conditions during the cumulus, mature, and dissipating stages of thunderstorm development.
- Describe how lightning forms.
- Describe the conditions necessary and location for hurricane development.
- Describe the potential impact of global warming on severe weather.
"Forecast for this evening...dark" - George Carlin
Weather is the day-to-day state of the atmosphere. The weather of the humid tropics is very similar throughout the year as a constant flow of energy keeps temperatures uniformly high. However, the daily weather is quite variable in the midlatitudes. Here, huge air masses collide to create powerful storm systems that affect global heat distribution, the shaping of the earth surface, and our daily livelihood. In this chapter we'll examine weather systems at a variety of geographic scales that affect our daily lives.
See if you are prepared for this chapter by "8.0: Getting Ready for Chapter 8"
-
- 8.5: Weather and Wave Cyclones
- The weather associated with the passage of a wave cyclone is a product of the convergence and frontal uplift found in the system. The wave cyclone can be divided into three sectors: (1) the cool sector ahead of the warm front, (2) the warm sector between the cold and warm fronts, and (3) the cold sector located behind the cold front.


14.11: Creating Basic Forms
Learning Outcomes
- Create basic forms
Access makes it relatively easy to create a basic form.
- Select the table or query containing the data you are interested in seeing on your form in the Navigation pane.
- Go to the Create tab, and the Forms group and select Form .
Access will create a basic form and open it in Layout view. You should be able to see the data you selected. In Layout view, you have some limited capabilities to make design changes to the form.
In addition to creating a basic form, Access will check to see if there are one-to-many relationships existing between the table you selected to create the form and any other tables in the database. If so, it will add a datasheet based on the related table or query to your basic form. For example, if you create a basic form based on the Customers table, and there is a one-to-many relationship with the Orders table, Access will display all of the records in the Orders table that relate to the Customers table in Datasheet view.
Learn More
For detailed, step-by-step instructions Microsoft Access Help is an excellent resource and can be found by following this link: MS Access Help: Creating Forms


3.3: Rates of Change and Behavior of Graphs
Learning Objectives
- Find the average rate of change of a function.
- Interpret average rate of change as the slope of a secant line.
- Use a graph to determine where a function is increasing, decreasing, or constant.
- Use a graph to locate local and global extrema.
Gasoline costs have experienced some wild fluctuations over the last several decades. Table \(\PageIndex{1}\) lists the average cost, in dollars, of a gallon of gasoline for the years 2005–2012. The cost of gasoline can be considered as a function of year.
| \(y\) | 2015 | 2016 | 2017 | 2018 | 2019 | 2020 | 2021 | 2022 |
|---|---|---|---|---|---|---|---|---|
| \(C(y)\) | 4.29 | 4.62 | 4.84 | 5.30 | 4.41 | 4.84 | 3.58 | 3.68 |
If we were interested only in how the gasoline prices changed between 2005 and 2012, we could compute that the cost per gallon had increased from $2.31 to $3.68, an increase of $1.37. While this is interesting, it might be more useful to look at how much the price changed per year. In this section, we will investigate changes such as these.
Finding the Average Rate of Change of a Function
The price change per year is a rate of change because it describes how an output quantity changes relative to the change in the input quantity. We can see that the price of gasoline in Table \(\PageIndex{1}\) did not change by the same amount each year, so the rate of change was not constant. If we use only the beginning and ending data, we would be finding the average rate of change over the specified period of time. To find the average rate of change, we divide the change in the output value by the change in the input value.
\[\begin{align*} \text{Average rate of change}&=\dfrac{\text{Change in output}}{\text{Change in input}} \\[4pt] &=\dfrac{\Delta y}{\Delta x}\\[4pt] &= \text{Slope of the Secant Line between } (x_1, y_1) \text{ and } (x_2,y_2)\\[4pt] &=\dfrac{y_2-y_1}{x_2-x_1}\\[4pt] &=\dfrac{f(x_2)-f(x_1)}{x_2-x_1}\end{align*} \label{1.3.1}\]
The Greek letter \(\Delta\) (delta) signifies the change in a quantity; we read the ratio as “delta-\(y\) over delta-\(x\)” or “the change in \(y\) divided by the change in \(x\).” Occasionally we write \(\Delta f\) instead of \(\Delta y\), which still represents the change in the function’s output value resulting from a change to its input value. It does not mean we are changing the function into some other function.
In our example, the gasoline price increased by $1.37 from 2005 to 2012. Over 7 years, the average rate of change was
\[\dfrac{\Delta y}{\Delta x}=\dfrac{$1.37}{7 \text{years}}\approx \text{0.196 dollars per year.} \label{1.3.2}\]
On average, the price of gas increased by about 19.6¢ each year. Other examples of rates of change include:
- The price of gasoline decreasing by 22 cents per year.
- A population of coyotes increasing by 40 coyotes per week.
- A car traveling 68 miles per hour.
- A vehicle fuel efficiency of 27 miles per gallon.
Definition: Rate of Change
A rate of change describes how an output quantity changes relative to the change in the input quantity. The units on a rate of change are “output units per input units.”
The average rate of change between two input values is the total change of the function values (output values) divided by the change in the input values.
\[\dfrac{\Delta y}{\Delta x}=\dfrac{f(x_2)-f(x_1)}{x_2-x_1}\]
How To...
Given the value of a function at different points, calculate the average rate of change of a function for the interval between two values \(x_1\) and \(x_2\).
- Calculate the difference \(y_2−y_1=\Delta y\).
- Calculate the difference \(x_2−x_1=\Delta x\).
- Find the ratio \(\dfrac{\Delta y}{\Delta x}\).
Example \(\PageIndex{1}\): Computing an Average Rate of Change
Using the data in Table \(\PageIndex{1}\), find the average rate of change of the price of gasoline between 2017 and 2019.
Solution
In 2017, the price of gasoline was $4.84. In 2019, the cost was $4.41. The average rate of change is
\[\begin{align*} \dfrac{\Delta y}{\Delta x}&=\dfrac{y_2−y_1}{x_2−x_1} \\[4pt] &=\dfrac{$2.41−$2.84}{2019−2017} \\[4pt] &=\dfrac{−$0.43}{2 \text{ years}} \\[4pt] &=−$0.22 \text{ per year} \end{align*}\]
Analysis
Note that a decrease is expressed by a negative change or “negative increase.” A rate of change is negative when the output decreases as the input increases or when the output increases as the input decreases.
Exercise \(\PageIndex{1}\)
Using the data in Table \(\PageIndex{1}\), find the average rate of change between 2015 and 2020.
- Solution
-
\(\dfrac{$4.84−$4.29}{5 \text{ years}} =\dfrac{$0.55}{5 \text{ years}} =$0.11 \text{per year.}\)
Example \(\PageIndex{2}\): Computing Average Rate of Change from a Graph
Given the function \(g(t)\) shown in Figure \(\PageIndex{1}\), find the slope of the secant line between the points \((−1,g(-1))\) and \(2,g(2))\)
Solution
At \(t=−1\), Figure \(\PageIndex{2}\) shows \(g(−1)=4\). At \(t=2\),the graph shows \(g(2)=1\).
The horizontal change \(\Delta t=3\) is shown by the red arrow, and the vertical change \(\Delta g(t)=−3\) is shown by the turquoise arrow. The output changes by –3 while the input changes by 3, giving an average rate of change of
\[\dfrac{1−4}{2−(−1)}=\dfrac{−3}{3}=−1\]
Analysis
Note that the order in which we evaluate is very important. For example, if we evaluated \(\dfrac{y_2−y_1}{x_1−x_2}\), we will not get the correct answer.
You must decide which point will have subscript 1 and which point will have a subscript 2, then BE CONSISTENT when evaluating by subtracting in the SAME ORDER each time.
Example \(\PageIndex{3}\): Computing Average Rate of Change from a Table
After picking up a friend who lives 10 miles away, Anna records her distance from home over time. The values are shown in Table \(\PageIndex{2}\). Find her average speed over the first 6 hours.
| \(t\) (hours) | 0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 |
|---|---|---|---|---|---|---|---|---|
| \(D(t)\) (miles) | 10 | 55 | 90 | 153 | 214 | 240 | 292 | 300 |
Solution
Here, the average speed is the average rate of change. She traveled 292 miles in 6 hours, for an average speed of
\[\begin{align*}\dfrac{292−10}{6−0}&=\dfrac{282}{6}\\[4pt] &= 47\end{align*}\]
The average speed is about 47 miles per hour.
Analysis
Because the speed is not constant, the average speed depends on the interval chosen. For the interval \([2,3]\), the average speed is 63 miles per hour.
Example \(\PageIndex{4}\): Computing Average Rate of Change for a Function Expressed as a Formula
Compute the average rate of change of \(f(x)=x^2−3x + 1\) on the interval \([2, 4]\).
Solution
We can start by computing the function values at each endpoint of the interval.
\[\begin{align*}f(2)&=2^2−3(2)+1 \\[4pt] &=4 - 6 + 1 \\[4pt] &=-1\end{align*}\]
\[\begin{align*}f(4)&=4^2−3(4)+1 \\[4pt] &=16 - 12+1 \\[4pt] &=5\end{align*}\]
Now we compute the average rate of change.
\[\begin{align*}\text{AROC} &=\frac{f(4)−f(2)}{4−2} \\[4pt] &=\frac{5-(-1)}{4-2} \\[4pt] &=\frac{5+1}{2} \\[4pt] &=3\end{align*}\]
Exercise \(\PageIndex{2}\)
Find the average rate of change of \(f(x)=\frac{1}{3x+1}\) on the interval \([0, 1]\).
- Solution
-
AROC = \(-\frac{3}{4}\)
Example \(\PageIndex{5}\): Finding an Average Rate of Change as an Expression
Find the average rate of change of \(g(t)=t^2+3t+1\) on the interval \([a, a+h]\). The answer will be an expression involving \(a\).
Solution
We use the average rate of change formula.
\(\begin{align*}\text{Average rate of change} &=\dfrac{g(a+h)−g(a)}{a+h-a} & \text{Evaluate.} \\[4pt] &=\dfrac{(a^2+ 2ah + h^2 + 3a + 3h+1)−(a^2+3a+1)}{h} & \text{Simplify.} \\[4pt] &=\dfrac{h^2+2ah + 3h}{h} & \text{Simplify and factor.}\\[4pt] &= \dfrac{h(h+2a + 3)}{h} & \text{Divide by the common factor h}\\[4pt] &= h+ 2a+3 \end{align*}\)
This result tells us the average rate of change between \(t_1=a\) and any other point \(t_2=a+h\) is equal to \(h+ 2a+3\)
For example, on the interval \([1,1+h]\), the average rate of change would be \(h+2(1) + 3 = h + 5\) where \(h\) represents the horizontal distance between \(t_1\) and \(t_2\)
Exercise \(\PageIndex{3}\)
Find the average rate of change of \(f(x)=x^2+2x−8\) on the interval \([a, a+5]\).
- Solution
-
AROC = \(2a+7\)
Using a Graph to Determine Where a Function is Increasing, Decreasing, or Constant
As part of exploring how functions change, we can identify intervals over which the function is changing in specific ways. We say that a function is increasing on an interval if the function values increase as the input values increase within that interval. Similarly, a function is decreasing on an interval if the function values decrease as the input values increase over that interval. The average rate of change of an increasing function is positive, and the average rate of change of a decreasing function is negative. Figure \(\PageIndex{3}\) shows examples of increasing and decreasing intervals on a function.
While some functions are increasing (or decreasing) over their entire domain, many others are not. A value of the input where a function changes from increasing to decreasing (as we go from left to right, that is, as the input variable increases) is called a local maximum . If a function has more than one, we say it has local maxima. Similarly, a value of the input where a function changes from decreasing to increasing as the input variable increases is called a local minimum . The plural form is “local minima.” Together, local maxima and minima are called local extrema , or local extreme values, of the function. (Fun Fact: The singular form of extrema is “extremum”)
Often, the term local is replaced by the term relative .
A function that is neither increasing nor decreasing on an interval is called constant . The graph would be a horizontal line.
A function is also neither increasing nor decreasing at the extrema.
For the function whose graph is shown in Figure \(\PageIndex{4}\), the local maximum is 16, and it occurs at \(x=−2\). The local minimum is −16 and it occurs at \(x=2\).
To locate the local maxima and minima from a graph, we need to observe the graph to determine where the graph attains its highest and lowest points, respectively, within an open interval. Like the summit of a roller coaster, the graph of a function is higher at a local maximum than at nearby points on both sides. The graph will also be lower at a local minimum than at neighboring points. Figure \(\PageIndex{5}\) illustrates these ideas for a local maximum.
Note: We must speak of these values as local extrema, because any given local extremum as defined here is not necessarily the highest maximum or lowest minimum in the function’s entire domain.
These observations lead us to the formal definitions of increasing, decreasing and constant and a formal definition of local extrema.
Increasing, Decreasing, Constant.
- A function \(f\) is increasing on an open interval if \(f(b)>f(a)\) for every \(a\), \(b\) interval where \(b>a\).
- A function \(f\) is decreasing on an open interval if \(f(b)<f(a)\) for every \(a\), \(b\) interval where \(b>a\).
- A function \(f\) is constant on open interval if \(f(b)=f(a)\) for every \(a\), \(b\) interval where \(b>a\).
Local Minima and Local Maxima
- A function \(f\) has a local maximum of \(f(b)\) at \(x = b\) in an open interval \((a,c)\) if \(f(b)\) is greater than or equal to \(f(x)\) for every \(x\) in the interval (\(x\) does not equal \(b\))
- Similarly, \(f\) has a local minimum of \(f(b)\) at \(x = b\) in \((a,c)\) if \(f(b)\) is less than or equal to \(f(x)\) for every \(x\) in the interval (\(x\) does not equal \(b\))
Example \(\PageIndex{7}\) Finding Increasing and Decreasing Intervals on a Graph
Given the function \(p(t)\) in Figure \(\PageIndex{6}\), identify the intervals on which the function appears to be increasing.
Solution
We see that the function is not constant on any interval. The function is increasing where it slants upward as we move to the right and decreasing where it slants downward as we move to the right. The function appears to be increasing from \(t=1\) to \(t=3\) and from \(t=4\) on.
In interval notation, we would say the function appears to be increasing on the interval \((1,3)\) and the interval \((4,\infty)\).
Analysis
Notice in this example that we used open intervals (intervals that do not include the endpoints), because the function is neither increasing nor decreasing at \(t=1\), \(t=3\), and \(t=4\). These points are the local extrema (two minima and a maximum).
Example \(\PageIndex{8}\)
The graph the function \(f(x)=x^3−6x^2−15x+20\) is shown in Figure \(\PageIndex{7}\)
Estimate the local extrema of the function. Use these to determine the intervals on which the function is increasing and decreasing.
- Solution
-
The local maximum appears to occur at \((−1,28)\), and the local minimum occurs at \((5,−80)\). The function is increasing on \((−\infty,−1)\cup(5,\infty)\) and decreasing on \((−1,5)\).
Figure \(\PageIndex{7}\) Graph of a polynomial with a local maximum at (-1, 28) and local minimum at (5, -80).
Example \(\PageIndex{9}\): Finding Local Maxima and Minima from a Graph
For the function f whose graph is shown in Figure \(\PageIndex{8}\), find all local maxima and minima.
Solution
Observe the graph of \(f\). The graph attains a local maximum at \(x=1\) because it is the highest point in an open interval around \(x=1\).The local maximum is the y-coordinate at \(x=1\), which is 2.
The graph attains a local minimum at \(x=−1\) because it is the lowest point in an open interval around \(x=−1\). The local minimum is the y-coordinate at \(x=−1\), which is −2.
Use A Graph to Locate the Absolute Maximum and Absolute Minimum
There is a difference between locating the highest and lowest points on a graph in a region around an open interval (locally) and locating the highest and lowest points on the graph for the entire domain. The y-coordinates (output) at the highest and lowest points are called the absolute maximum and absolute minimum , respectively. To locate absolute maxima and minima from a graph, we need to observe the graph to determine where the graph attains it highest and lowest points on the domain of the function.
Often, the term absolute is replaced by the term global .
(Figure \(\PageIndex{9}\)).
Not every function has an absolute maximum or minimum value. For example the function \(f(x) = x^2\) does NOT have an absolute maximum.
Absolute Maxima and Minima
- The absolute maximum of \(f\) at \(x=c\) is \(f(c)\) where \(f(c)≥f(x)\) for all \(x\) in the domain of \(f\).
- The absolute minimum of \(f\) at \(x=d\) is \(f(d)\) where \(f(d)≤f(x)\) for all \(x\) in the domain of \(f\).
Example \(\PageIndex{10}\): Finding Absolute Maxima and Minima from a Graph
For the function f shown in Figure \(\PageIndex{10}\), find all absolute maxima and minima.
Solution
Observe the graph of \(f\). The graph attains an absolute maximum in two locations, \(x=−2\) and \(x=2\), because at these locations, the graph attains its highest point on the domain of the function. The absolute maximum is the y-coordinate at \(x=−2\) and \(x=2\), which is 16.
The graph attains an absolute minimum at x=3, because it is the lowest point on the domain of the function’s graph. The absolute minimum is the y-coordinate at x=3,which is−10.
Example \(\PageIndex{11}\): Finding Absolute Maxima and Minima from a Graph
For the function f shown in Figure \(\PageIndex{11}\), find all absolute maxima and minima.
Solution
Observe the graph of \(f\)T, the implied domain is \((-oo,oo)\).
The absolute maximum does not exist because there is no point on this graph for which the value of \(f(x)\) is greater than all other values for every \(x\) in the implied domain.
The graph attains an absolute minimum is the y-coordinate at \(x=1\), which is \(y = 0\) , because \(f(1) = 0 \) and \(0 ≤ f(x)\) for all possible \(x\) in the domain of the function.
Answers
The absolute minimum is \(0\) at \(x=1\).
The absolute maximum does not exist, we would enter DNE for this part of the answer.
Key Equation
- Average rate of change: \(\dfrac{\Delta y}{\Delta x}=\dfrac{f(x_2)-f(x_1)}{x_2-x_1}\)
Key Concepts
- A rate of change relates a change in an output quantity to a change in an input quantity. The average rate of change is determined using only the beginning and ending data. See Example.
- Identifying points that mark the interval on a graph can be used to find the average rate of change. See Example.
- Comparing pairs of input and output values in a table can also be used to find the average rate of change. See Example.
- An average rate of change can also be computed by determining the function values at the endpoints of an interval described by a formula. See Example and Example.
- The average rate of change can sometimes be determined as an expression. See Example.
- A function is increasing where its rate of change is positive and decreasing where its rate of change is negative. See Example.
- A local maximum is where a function changes from increasing to decreasing and has an output value larger (more positive or less negative) than output values at neighboring input values.
- A local minimum is where the function changes from decreasing to increasing (as the input increases) and has an output value smaller (more negative or less positive) than output values at neighboring input values.
- Minima and maxima are also called extrema.
- We can find local extrema from a graph. See Example and Example.
- The highest and lowest points on a graph indicate the maxima and minima. See Example.


8.2: Whoso List to Hunt
By Sir Thomas Wyatt
Whoso list to hunt? I know where is an hind!
But as for me, alas! I may no more,
The vain travail hath wearied me so sore;
I am of them that furthest come behind.
Yet may I by no means my wearied mind
Draw from the deer; but as she fleeth afore
Fainting I follow; I leave off therefore,
Since in a net I seek to hold the wind.
Who list her hunt, I put him out of doubt
As well as I, may spend his time in vain!
And graven with diamonds in letters plain,
There is written her fair neck round about;
“ Noli me tangere ; for Cæsar’s I am,
And wild for to hold, though I seem tame.”
- Whoso List to Hunt. Authored by : Sir Thomas Wyatt. Provided by : The Saylor Foundation. Located at : http://www.saylor.org/site/wp-content/uploads/2011/05/ENGL202-3.1.1-Whosolist.pdf . License : CC BY: Attribution
- Whoso List to Hunt - Sir Thomas Wyatt. Authored by : Rumpoleful. Located at : https://youtu.be/rLfNiaHforg . License : All Rights Reserved . License Terms : Standard YouTube License


Abstract.
The renaissance of board games in the digital age is sometimes attributed to the multiplication of board game channels on Youtube (Muench, 2017), or to the need to socialize and interact in person (Jolin, 2016). Today, board gameplay is not only livestreamed on platforms such as
Twitch
.
Tv
, but sites such as
boardgame
g
eek
, and gaming conventions such as
Gen Con
create a space for board gamers to interact and keep up with the latest happening in the board game community/industry. . Though board gameplay is breaking into mainstream, studies on the different learning spaces in the digital era are still dominated by environments enriched with digital tools such as video games (Carter, Gibbs & Harrop, 2014a). Drawing on board game literature, this chapter discusses board games and how the resurgence of these games in the 21st century may provide an opportunity to understand learning in the digital age.
Introduction.
The rising trend of board gameplay in recent years puzzles many observers of the popular culture. In a technology-driven society, and in a time when important interactions are preferably delegated to technology (Turkle, 2012), the revival of board games (Graham, 2016) is intriguing as well as interesting. According to Euromonitor International, a global market research firm, the global sales of board games reached $9.6 billion in 2016, with board games such as Settlers of Catan selling more than $80 million in the United States (Graham, 2016). Board games are becoming for families, children, and young adults, a way to socialize and a common entertainment (Graham, 2016). Kay (2018) writes that U.S. sales of board games increased by 28% between 2016 and 2017 and will grow at a similar rate by 2020. The resurgence of board games in this age certainly denotes a need to explore the revival of board games in the United States in the era of video games. Paraphrasing James Gee, in this chapter, I interrogate board gameplay in an attempt to address the following question: what do board games have to tell us about learning in the digital age?
Oxford online dictionary defines board games as games that include the movement of counters or other objects round a board. These games are certainly different from video games because they include moving pieces on a premarked physical board (Berland & Lee, 2011). It should be noted that some board games such as
Mysterium
,
Songo
,
Oware
, Through the Ages: A New Story of Civilization, and Lords of
Waterdeep
have been digitized (Ekwè, 2005; Marks & Thrower, 2018). Yet, the board game renaissance is driven by children and adults (Jolin, 2016; Kay, 2018). Furthermore, the development of games such as German-style board games
1
(e.g.,
Settlers of
Catan
and
Pandemic
) that prioritize action and encourage the optimization of limited resources (Kapp, 2018), also explain this resurrection.
Prior to discussing the relationship between board games and learning in the digital age, it is critical to explain that the notion of board game resurgence in this century is specific to the Western world (e.g., United States, United Kingdom, Canada, Germany). In Africa, and particularly in Cameroon, board gameplay has been a popular activity for centuries, and as such, the notion of board game resurgence in the digital age may not be applied to Africa, and specifically to Cameroon. The digital age refers to the wide use of digital technology in almost all aspects of human activities, including economic, social, and political interactions (Adomi, 2008; Wang & Torrisi-Steele, 2016). In other words, the digital age is characterized by digital technology shaping the way people live and interact (Ngelime, 2018). Though Africa has creatively embraced the digital age and can no longer be viewed as out of digital age world (Ngelime, 2018), board games have always been popular in different communities or ethnic groups (Nxumalo & Mncube, 2018).
Learning and board games in the digital age
Despite the resurgence of board games, they are mostly researched as artifacts or objects of art , and not as spaces for learning (Bayeck, 2017; Wise, 2018). Nevertheless, some researchers have started exploring board games as learning spaces (Berland & Lee, 2012; Carter et al., 2014) to uncover their learning potential (Bayeck, 2017; Carter, Harrop & Gibbs, 2014a). Such research deviates from the long-standing tradition in game studies that conceived board games as spaces to mine for the design of digital games to enhance players’ gaming experiences (Xu, Barba, Radu, Gandy & MacIntyre, 2011; Zagal, Rick & Hsi, 2006). As Carter et al. (2014b) explain:
The limited number of studies which solely focus on the attraction and experience of non-digital games presents the possibility that without a firm foundational understanding of the [board game] game experience, and the role that the physicality of this experience plays in the enjoyment of the game (highlighted as being important), essential elements of the experience may be overlooked or diminished in digital augmentation (p. 7).
Consequently, without an examination of board gameplay, the learning experiences board games offer to players are likely to be overlooked. In the following paragraphs, I discuss few studies on board games to highlight learning occurring in board gameplay, and to point to board games as spaces for learning that is relevant in the 21
st
century.
In their study of Warhammer 40,000
2
(W40K) board game, Carter et al. (2014a) described players’ multiple activities that evidenced critical thinking, as well as strategic thinking. For instance, players researched narratives behind each army prior to drafting their army by using external resources such as books developed by the developers of the game (Carter et al., 2014a). Players also studied the characters prior to drafting their army by using fictional books about the game, and simulated their readings during their gameplay (Carter et al., 2014a). In addition, players developed their own gameplay strategy based on their preconception of how the game will unfold (Carter et al., 2014a). I argue that W40K practices as described in Carter et al. (2014a) involved a learning process that increased gameplay experience and motivation. For example, in researching players and the different armies’ narratives, players acquired research skills, while gaining more information about the characters and the armies. Playing also meant engaging in decision-making (e.g., drafting the army), and in strategic thinking as they created their own gameplay strategy (Carter et al., 2014a). Though a pastime, W40K activities engage players in learning that is pleasant and fun. Hence, the process of selecting characters, building the army, and using external resources is an illustration of players’ engagement in contextualized meaning making practices, or literacy practices. Indeed, from a sociocultural perspective, participation in practices related to the gameplay as well as interacting with others is learning (Lantolf, 2000; Nasir & Hand, 2006).
Berland and Lee (2012) explored
Pandemic
3
(Figure 2), a collaborative board game in which players team up to fight diseases and keep the world safe. The authors show that players engaged in complex computational thinking activities distributed among participants (Berland & Lee, 2012). For instance, players collaborated to understand their actions, and engaged in significant crosstalk during gameplay (Berland & Lee, 2012). Consequently,
Pandemic
created a space for players to participate in learning activities that included computational thinking practices, and collaboration. Board games are therefore useful spaces for learning and practicing skills that are important for everyday life in the digital age.
With regards to learning, it is important to also consider non-western board games. However, empirical studies of board games and learning in non-western contexts such as Africa are still extremely limited (Bayeck, 2017; Mkondiwa, 2019). Nevertheless, as mentioned earlier, the notion of resurgence of board games in the digital age cannot unquestionably be applied to Africa. Africa has a long tradition of board gameplay. Board games such as
Oware
,
Songo
,
and
Bao
(Bayeck, 2017; BBC, 2016; Mawere, 2013) are ancient African board games that require “high degree of intelligence and vigilance when playing [them]” (Mawere, 2013, p.11). According to Mawere (2013) board gameplay constituted one of the educational strategies used in precolonial Africa. Though empirical studies on African board gameplay are practically nonexistent, description of strategic games such as
Songo
4
(Figure 3) evidences that the gameplay involves complex thinking and strategies to outwit the adversary (Meka, 2008; Owona, 2004).
Songo
gameplay involves the use of proverbs as a means to demonstrate players’ level of expertise, fast and complex calculations (Njock, 1985; Mbarg Owona, 2004). Building on Owona’s (2004) and Njock’s (1985) descriptions of the gameplay, it is clear that
Songo
gameplay involves practices that create learning opportunities for players. For instance, counting seeds/pebbles, strategizing to beat the opponent, and engaging in an exchange of proverbs (implying communication as well as language learning) are instances of learning and literacy practices embedded in this ancient African game that are relevant in the digital age. Hence, as competitiveness, strategy, and communication are critical in Songo gameplay, so are these ideas important in the digital age. Reflecting on another board game called
Tsoro
5
(Figure 4), Mawere (2013) writes:
In fact the players have to think quickly and clearly in order to outwit the opponent. This means that the game is meant to develop and sharpen the [player’s] intellectual faculty such that s/he [develops] the aptitude to manoeuvre different situations in real life. (p.11).
Drawing from the discussion above, there is no doubt that exploring board gameplay is relevant for understanding learning in the digital age. Indeed, non-digital environments such as board games can allow for learning skills that have been strongly associated with digital technology (e.g., computational thinking). Moreover, board games tell us that learning in the digital age is also about interactions, and community. Players value the social component of board games that allows in-person interaction, and reduces isolation (Graham, 2016; Jolin, 2016). Considering that learning occurs in this space, I argue that learning is facilitated in environments that allow, or are designed for interactions to happen among learners, and for spaces that limit the isolation of individuals in the learning process. While Peerutin (2017) views the rise of board games as a counterpoint to the digital trend, a “desire to switch off from the harsh and anxiety-producing reality of the real world”, I argue that the resurgence can shape learning in this age. Quoting a player, Matson (2018) writes:
While the internet is a great thing, sitting down and playing with friends and family is becoming increasingly important. Having time away from our phones and computers where we can talk, play and enjoy time together is something board games let us do.
A first glance at this statement seems to indicate that board game players want to stay away from digital technologies. However, a closer look at this statement also unravels a desire to interact, to be in an environment that enhances togetherness. This understanding is for instance supported by the livestreaming of board gameplay on
Twitch.Tv
, which shows that staying away from digital tools, is not the only and predominant attraction of board games for players. The social component of board games can inform the design of learning settings in the 21st century.
Conclusion
With the resurgence of board games, especially in the Western world, in the era of social media, digital games, and other forms of digitally-mediated human interactions, I discuss in this chapter learning in the digital age through board games. I contend that limiting the rise of board games to the need for players to interact in person, away from digital tools, may prevent researchers, designers, and educators from engaging with what that may mean for learning in the era of digital technology. The revival of board games gives us insights into learning and learners today; it tells us about learning in the digital age. As much as digital games’ popularity has drawn the interest of educational researchers, the rise of board games in the digital era calls for greater exploration of learning in these spaces, and their potential to inform learning, and the design of learning settings in this age.
Bayeck, R. Y. (2017). A review of five African board games: is there any educational potential?
Cambridge Journal of Education
, 1–20. doi:10.1080/0305764x.2017.1371671
Berland, M., & Lee, V. (2011). Collaborative strategic board games as a site for distributed computational thinking.
International Journal of Game-Based Learning, 1
(2), 65–81.
Berland, M., Lee, V. (2012). Collaborative strategic board games as a site for distributed computational thinking.
International Journal of Game-Based Learning, 1
(2), 65–81
Harrop, M., Gibbs, M. & Carter, M. (2013). Everyone’s a winner at Warhammer 40K (or, at least not a loser).
In Proceedings of the
DiGRA
2013
Conference:
DeFragging
Game
Studies
. Atlanta, GA.
Mawere, M. (2013). Child education in pre-colonial Africa: Lessons from traditional strategies used to raise and educate children in pre-colonial Zimbabwe. InM. Mawere & P. Rambe, P. (eds.),
Leveraging educational quality in southern African educational systems: A practitioners’ perspective
(pp. 5-22). Mankon, Bamenda, Cameroon: Langaa Research & Pub. CIG.
Meka, O. J.M. (2008).
Le
jeu
du
Songo
:
Reflets
du
social
. Cameroun: L’Harmattan
Mkondiwa, M. (2019). Games of strategy in culture and economics research.
Journal of Economic Methodology
, 1–18. doi:10.1080/1350178x.2019.1680858
Nasir, N. I. S., & Hand, V. M. (2006). Exploring sociocultural perspectives on race, culture, and learning.
Review of Educational Research
,
76
(4), 449-475.
Njock, G. E. (1985). Mathématiques et environnement socio-culturel en Afrique Noire.
Présence
Africaine
, 3
, 3-21.
Nxumalo, S. A., & Mncube, D. W. (2018). Using indigenous games and knowledge to decolonise the school curriculum: Ubuntu perspectives.
Perspectives in Education, 36
(2), 103–118
Owona, S. M. (2004).
Le
jeu
de
Songo
. Paris, France: L’Harmattan.
Turkle, S. (2012).
Alone together: Why we expect more from technology and less from each other
. New York: Basic Books
Wang, V. X., & Torrisi-Steele, R. (2016). Reflective Learning in the Digital Age: Insights from Confucius and Mezirow. In V. Wang (Ed.),
Handbook of Research on Learning Outcomes and Opportunities in the Digital Age
(pp. 421-440). Hershey, PA: IGI Global.
Xu, Y., Barba, E., Radu, I., Gandy, M. & MacIntyre, B. (2011). Chores are fun: Understanding Social Play in Board Games for Digital Tabletop Game Design. In
Proceedings of The 5th International Digital Games Research Conference
. Hilversum, The Netherlands: DiGRA.
Zagal, J. P., Rick, J., & Hsi, I. (2006). Collaborative games: Lessons learned from board games.
Simulation & Gaming
,
37
(1), 24-40.
1
German-style board games are characterized by strategy, economics, cooperation, military themes, and the downplaying of luck (Lamb, 2011; Kapp, 2018).
2
A strategic game created by Games Workshop Ltd; its success has led to the development of various derivative products.
3
A game published by Z-Man Games in 2007. Pandemic is one of the key titles in the board-gaming resurrection, and the collaborative aspect of the game the world attracts a wide range of players (Jolin, 2016).
4
Songo
is made of two rows of seven holes each on a long wooden board. It is played with 70 identical seeds/pebbles distributed equally between two players, and the player with 40 seeds/pebbles wins the game (Meka, 2008; Owona, 2004). There are different versions of
Songo
game across Africa, as well as different rules. The winning principle mentioned here is specific to
Songo
played by the Ewondo ethnic group in Cameroon.
5
Mostly played in Southern Africa, made of four rows of 32 holes, and played with 64 seeds/pebbles


3.2.1: Minimization Applications (Exercises)
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For each of the following minimization problems, choose your variables, write the objective function and the constraints, graph the constraints, shade the feasibility region, label all critical points, and determine the solution that optimizes the objective function.
1) A diet is to contain at least 2400 units of vitamins, 1800 units of minerals, and 1200 calories. Two foods, Food A and Food B are to be purchased. Each unit of Food A provides 50 units of vitamins, 30 units of minerals, and 10 calories. Each unit of Food B provides 20 units of vitamins, 20 units of minerals, and 40 calories. Food A costs $2 per unit and Food B cost $1 per unit. How many units of each food should be purchased to keep costs at a minimum?
2) A computer store sells two types of computers, laptops and desktops. The supplier demands that at least 150 computers be sold a month. Experience shows that most consumers prefer laptops, but some business customers require desktops. The result is that the number of laptops sold is at least twice of the number of desktops. The store pays its sales staff a $60 commission for each laptop, and a $40 commission for each desktop. Let \(x\) = the number of laptops and \(y\) = the number of desktop computers. How many of each type must be sold to minimize commission to its sales people?
What is the minimum commission?
3) An oil company has two refineries. Each day, Refinery A produces 200 barrels of high-grade oil, 300 barrels of medium-grade oil, and 200 barrels of low-grade oil and costs $12,000 to operate. Each day, Refinery B produces 100 barrels of high-grade oil, 100 barrels of medium-grade oil, and 200 barrels of low-grade oil and costs $10,000 to operate. The company must produce at least 800 barrels of high-grade oil, 900 barrels of medium-grade oil, and 1,000 barrels of low-grade oil.
How many days should each refinery be operated to meet the goals at a minimum cost?
4) A print shop at a community college in Cupertino, California, employs two different contractors to maintain its copying machines. The print shop needs to have 12 IBM, 18 Xerox, and 20 Canon copying machines serviced. Contractor A can repair 2 IBM, 1 Xerox, and 2 Canon machines at a cost of $800 per month, while Contractor B can repair 1 IBM, 3 Xerox, and 2 Canon machines at a cost of $1000 per month. How many months should each of the two contractors be employed to minimize the cost?


5: Newton’s Laws
- Understand Newton’s Three Laws.
- Understand the concept of force and how to identify a force.
- Understand the concepts of mass and inertia.
- Understand how to draw free-body diagrams.
In this chapter, we introduce Newton’s Laws, which is a succinct theory of physics that describes an incredibly large number of phenomena in the natural world. Newton’s Laws are one possible formulation of what we call “Classical Physics” (as opposed to “Modern Physics” which include Quantum Mechanics and Special Relativity). Newton’s Laws make the connection between dynamics (the causes of motion) and the kinematics of motion (the description of that motion).
 To keep the cart moving, you notice that you have to keep applying a force to the cart. You conclude that a continuous force is needed for continuous motion. This statement is,
- True, since the natural state of all objects is to be at rest. Eventually, all objects will be at rest, so to keep an object moving, a force needs to be applied.
- False. The force you apply to keep an object moving is only to counteract a frictional force.


About this Chapter
This chapter explores the many ways your health is impacted by your lifestyle choices. The goal of this material is to help you do the following:
-
- Describe actions you can take to improve your physical health.
-
- Identify ways to maintain and enhance your emotional health.
-
- Understand mental health risks and warning signs.
-
- Articulate reasons and ways to maintain healthy relationships.
-
- Outline steps you can take to be more safety conscious.
Recent headlines were buzzing with news about a 17-year-old boy who lost his eyesight because of a poor diet. While the boy ate enough food and his weight was considered normal, when doctors investigated, they discovered he didn’t eat enough
nutrient
-
rich
food. A self-described picky eater, the teen’s daily diet consisted of sausage, deli ham, white bread, Pringles, and french fries. His food choices led to numerous nutritional deficiencies of several essential vitamins and minerals, causing nutritional optic neuropathy.
1
Have you heard the saying “you are what you eat”?  Are we really what we eat, and what does this phrase actually mean? While the example of the boy who lost his vision may be extreme, the food we eat does impact our physical and mental health. What’s at the end of our fork can keep us healthy or eventually make us sick. Every 27 days, our skin replaces itself and our body makes new cells from the food we eat.
2
And according to Dr. Libby Weaver, every three months we completely rebuild and replace our blood supply.

There are two primary reasons we become unhealthy. First, we do not deliver enough nutrients for our cells to operate properly, and second, our cells are bombarded with too many toxins. Keeping it simple, good health is proper nutrients in, toxins out. Toxins come from a host of sources—certain foods, the environment, stressful relationships, smoking, vaping, and alcohol and drug use. And if we don’t sleep and exercise enough, toxins can hang around long enough to cause us harm.
As a first-year college student you will make many choices without parental oversight, including the food you eat and the way you take care of your body and brain. Some choices put you on a path to health, and other choices can lead you down a path toward illness. There is a strong connection between success in college and your ability to stay healthy.
Health is more than a strong body that doesn’t get sick. Health also includes your overall sense of well-being (mental, emotional) and healthy relationships. Good health is about making positive choices in all of these areas, and avoiding destructive choices. It’s about learning to be smart, to set boundaries, to watch out for your safety, and to take care of the one body that will carry you through life.
While health and wellness are often interchanged, it is important to differentiate the two concepts.
Health is
a state of physical, mental, and social well-being, while
wellness
is a process through which people become aware of and make choices toward a healthy and fulfilling life.


18.4: Chapter Summary
Theories and models of health promotion, disease prevention, and behavior change are used in the development of community health programs. Common theories include the community action model, PRECEDE-PROCEED model, PATCH model, and intervention mapping. Logic models are created as a visual representation of a community program. SDOH and population learning needs are also considered. Health promotion and disease prevention approaches, such as the HBM, transtheoretical model, and SCT, are applied to motivate and promote program participant behavior change.
A participatory approach plays a key role in the success of community health programs. The nurse engages members of the target population, organizations, and other interested parties by creating partnerships and coalitions. The nurse uses various strategies to identify and recruit partners, such as social networking, community mapping, and partner analysis. Established program partners develop a shared vision, values, and capacity for the community health program. The team also considers ethical standards and potential ethical issues throughout program planning, implementation, and evaluation.
The final steps of program planning involve the creation of program goals, objectives, outcomes, and an action plan. Goals explain the program’s overarching purpose, and objectives describe specific actions that will lead to the achievement of program goals. Well-written objectives are SMART, include both process and outcomes, and have short-term, intermediate, and long-term time frames for achievement. The action plan is a step-by-step strategy for the implementation of evidence-based intervention. Healthy People 2030 can be used to search for relevant, current, and evidence-based interventions.


12.13.7: New Ideas
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A final trend that is emerging is a n extension of the Internet of Things: autonomous robots and vehicles. By combining software, sensors, and location technologies, devices that can operate themselves to perform specific functions are being developed. These take the form of creations such as medical nanotechnology robots (nanobots), self-driving cars, or unmanned aerial vehicles (UAVs).
A nanobot is a robot whose components are on the scale of about a nanometer, which is one-billionth of a meter. While still an emerging field, it is showing promise for applications in the medical field. For example, a set of nanobots could be introduced into the human body to combat cancer or a specific disease.
In March of 2012, Google introduced the world to their driverless car by releasing a video on YouTube showing a blind man driving the car around the San Francisco area. The car combines several technologies, including a laser radar system, worth about $150,000. While the car is not available commercially yet, three US states (Nevada, Florida, and California) have already passed legislation making driverless cars legal.
A UAV, often referred to as a “drone,” is a small airplane or helicopter that can fly without a pilot. Instead of a pilot, they are either run autonomously by computers in the vehicle or operated by a person using a remote control. While most drones today are used for military or civil applications, there is a growing market for personal drones. For around $300, a consumer can purchase a drone for personal use.