3.4: Energy Enters Ecosystems Through Photosynthesis
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Cells run on the chemical energy found mainly in carbohydrate molecules, and the majority of these molecules are produced by one process: photosynthesis. Through photosynthesis, certain organisms convert solar energy (sunlight) into chemical energy, which is then used to build carbohydrate molecules. The energy stored in the bonds to hold these molecules together is released when an organism breaks down food. Cells then use this energy to perform work, such as movement. The energy that is harnessed from photosynthesis enters the ecosystems of our planet continuously and is transferred from one organism to another. Therefore, directly or indirectly, the process of photosynthesis provides most of the energy required by living things on Earth. Photosynthesis also results in the release of oxygen into the atmosphere. In short, to eat and breathe humans depend almost entirely on the organisms that carry out photosynthesis.
Solar Dependence and Food Production
Some organisms can carry out photosynthesis, whereas others cannot. An autotroph is an organism that can produce its own food. The Greek roots of the word autotroph mean “self” (auto) “feeder” (troph). Plants are the best-known autotrophs, but others exist, including certain types of bacteria and algae (Figure \(\PageIndex{1}\)). Oceanic algae contribute enormous quantities of food and oxygen to global food chains. More specifically, plants are photoautotrophs , a type of autotroph that uses sunlight and carbon from carbon dioxide to synthesize chemical energy in the form of carbohydrates. All organisms carrying out photosynthesis require sunlight.
Heterotrophs are organisms incapable of photosynthesis that must therefore obtain energy and carbon from food by consuming other organisms. The Greek roots of the word heterotroph mean “other” ( hetero ) “feeder” ( troph ), meaning that their food comes from other organisms. Even if the organism being consumed is another animal, it traces its stored energy back to autotrophs and the process of photosynthesis. Humans are heterotrophs, as are all animals and fungi. Heterotrophs depend on autotrophs, either directly or indirectly. For example, a deer obtains energy by eating plants. A wolf eating a deer obtains energy that originally came from the plants eaten by that deer (Figure \(\PageIndex{2}\)). Using this reasoning, all food eaten by humans can be traced back to autotrophs that carry out photosynthesis.
Summary of Photosynthesis
Photosynthesis requires sunlight, carbon dioxide, and water as starting reactants (Figure \(\PageIndex{3}\)). After the process is complete, photosynthesis releases oxygen and produces carbohydrate molecules, most commonly glucose. These sugar molecules contain the energy that living things need to survive. The complex reactions of photosynthesis can be summarized by the chemical equation shown in Figure \(\PageIndex{4}\) below.
Although the equation looks simple, the many steps that take place during photosynthesis are actually quite complex. In plants, photosynthesis takes place primarily in the chloroplasts of leaves. Chloroplasts have a double (inner and outer) membrane. Within the chloroplast is a third membrane that forms stacked, disc-shaped structures called thylakoids. Embedded in the thylakoid membrane are molecules of chlorophyll , a pigment (a molecule that absorbs light) through which the entire process of photosynthesis begins.
The Two Parts of Photosynthesis
Photosynthesis takes place in two stages: the light-dependent reactions and the Calvin cycle . In the light-dependent reactions chlorophyll absorbs energy from sunlight and then converts it into chemical energy with the aid of water. The light-dependent reactions release oxygen as a byproduct from the splitting of water. In the Calvin cycle , the chemical energy derived from the light-dependent reactions drives both the capture of carbon in carbon dioxide molecules and the subsequent assembly of sugar molecules.
The Global Significance of Photosynthesis
The process of photosynthesis is crucially important to the biosphere for the following reasons:
- It creates O 2 , which is important for two reasons. The molecular oxygen in Earth’s atmosphere was created by photosynthetic organisms; without photosynthesis there would be no O 2 to support cellular respiration (see chapter 3.2 ) needed by complex, multicellular life. Photosynthetic bacteria were likely the first organisms to perform photosynthesis, dating back 2-3 billion years ago. Thanks to their activity, and a diversity of present-day photosynthesizing organisms, Earth’s atmosphere is currently about 21% O 2 . Also, this O 2 is vital for the creation of the ozone layer (see chapter 10.2 ), which protects life from harmful ultraviolet radiation emitted by the sun. Ozone (O 3 ) is created from the breakdown and reassembly of O 2 .
- It provides energy for nearly all ecosystems. By transforming light energy into chemical energy, photosynthesis provides the energy used by organisms, whether those organisms are plants, grasshoppers, wolves, or fungi. The only exceptions are found in very rare and isolated ecosystems, such as near deep sea hydrothermal vents where organisms get energy that originally came from minerals, not the sun.
- It provides the carbon needed for organic molecules. Organisms are primarily made of two things: water and organic molecules, the latter being carbon based. Through the process of carbon fixation, photosynthesis takes carbon from CO 2 and converts it into sugars (which are organic). Carbon in these sugars can be re-purposed to create the other types of organic molecules that organisms need, such as lipids, proteins, and nucleic acids. For example, the carbon used to make your DNA was once CO 2 used by photosynthetic organisms (see section 3.1 for more information on food webs).
Contributors and Attributions
- Essentials of Environmental Science by Kamala Doršner is licensed under CC BY 4.0 . Modified from the original by Matthew R. Fisher.


12.2: Cost-Plus or Target Costing Decisions
Learning Outcomes
- Create a report outlining the data to support a cost-plus pricing or target costing decision
Cost-plus pricing , is when a company figures out their total cost of a product and adds the profit as a “mark-up” above the cost. If a company has a more unique item, that consumers are willing to pay a premium for, cost-plus pricing can be effective. These companies are called PRICE-MAKERS. They get to decide, based on the fact that their item can be differentiated from other products on the market, and priced based on this justification.
So, if a company’s cost to make a widget is $5.00 and they want a 50% profit, they will charge $7.50 for the widget calculated as follows:
We can also look at cost plus pricing like this:
Total Costs + Desired Profit = Desired Revenue
$5.00 + ($5.00 x 50%)= $7.50
Target costing , involves looking at what the company wants for a profit, the price for the product that the market will bear, and then determines how to potentially cut costs to reach the desired profit. Products with a lot of competition, or that are not unique, may need to be priced in this manner. These companies are called PRICE-TAKERS. They need to price based on a market average, or to meet the pricing that the market will bear, due to other substitute products being available at the same or lower prices.
So in our widget example, it would be calculated in this way:
This concept looks like this:
Revenue − Desired Target Profit = Costs
($7.50 − $2.50 = $5.00)
When we look at this process, the pressure is put on the buyers at the company to find the lowest priced components in order to lower costs and create the desired profit for the company.
There is a great deal of pressure to keep costs low and profits high. In a competitive market, it may not be possible to get the desired profit without competitively pricing the item and then lowering costs through an effective purchasing system.
Some items, such as the fuchsia Hupana Running Company high tops, won’t have that pressure, but what if you sell paper clips? People may not be willing to pay more for a paper clip no matter how much you spend on your components, right?
Picking how to price your products, cost-plus pricing or target pricing will depend on the market for your product and what price the consumers are willing to pay.
Practice Questions


8.6: EFA Write Up
At the end of this section you should be able to answer the following questions:
- What are some common elements of a Results Section in an EFA write up?
- What are some common Tables included in an EFA write up?
Guide (only) to Writing the Results section
A brief guide for the result write-up is: What analysis was conducted and for what purpose (include extraction method, number of items, and number of participants or sample size, including a test of sampling adequacy). What were the outcomes from data screening. You should present results from the analysis (not describe the analysis), i.e. answer the research questions:
- The criterion for determining the number of components to extract
- Method of rotation
- Cut-off used for retaining items for interpretation
- Appraise the solution (e.g. are there distinct components or are there many items with cross pattern coefficients?)
- Describe the components and name the components
- Estimate the internal consistency of each component
- A full example write-up will be provided.
Guide to Table/s to be Included
For the tables you should include:
A summary of eigenvalue, the total variance accounted by each component, and the cumulative percentage of total variance accounted by the four components.
Also the items, pattern coefficients (in descending order), and communalities (indicate before rotation since they are values from the output) of the items.
See the EFA Example Write-Up .


1.5: Characterizing Emergency Management Activities
Before discussing the tasks that constitute emergency management, it is important to briefly ground the discussion in the process of accomplishing emergency management. There have been years of dialogue regarding “who really does emergency management”. Although the history just reviewed focuses largely on federal efforts, it is both accurate and appropriate to conceive of emergency management as a local endeavor to influence events with local consequences. This is in keeping with FEMA’s practice of attempting to make US emergency management a “bottom up” proposition. Of course, the job can be done optimally only with intergovernmental communication and cooperation that links local, state, and federal efforts. In some cases—for example, biological threats—the full resources of the federal government are needed to even begin the management process. Certainly in a major incident, external support (particularly state and federal) of many forms is made available to local jurisdictions. There is an inevitable time lag, however; currently the National Response Plan alerts local communities they must plan to operate without external help for approximately 72 hours after disaster impact. In addition, when external support does arrive, the response proceeds most efficiently and effectively if there is a strong, locally devised structure in place into which external resources can be integrated (Perry, 1985). Taking these realities into account, the tasks of emergency management can be discussed more effectively if there is a structure into which to fit the discussion.
The Local Emergency Management System
Figure \( \ref{1} \) describes the elements of a local emergency management system with some of its intergovernmental connections. By reviewing the figure, one can place in context some of the tasks and the tools available for emergency management. This chart is not intended to capture all actors and processes but, rather, to indicate the critical elements in the emergency management system. Ultimately, of course, the processes and tasks described here take place at every level of government.
The process of emergency management should be based on a careful hazard/vulnerability analysis (HVA) that identifies the hazards to which a community is exposed, estimates probabilities of event occurrence, and projects the likely consequences for different geographic areas, population segments, and economic sectors (Greenway, 1998; Ketchum & Whittaker, 1982). It is important to emphasize that HVA is not a static activity because hazards are not static. HVA is probably best conceptualized as a process that periodically reassesses the hazard environment so emergency managers can facilitate the challenging process of deciding which hazards are significant enough to require active management. This is a complex process that involves myriad considerations and input from a variety of actors; more detailed descriptions of this process are available in the work of Birkland (1997) and Prater and Lindell (2000).
Figure \( \PageIndex{1} \): Local Emergency Management System.
Hazard management decisions are influenced by multiple considerations. There are statutory and administrative mandates to manage certain hazards. The available hazard data, derived from national sources such as FEMA’s Multi-Hazard Identification and Risk Assessment (Federal Emergency Management Agency, 1997) and supplemented by local sources such as Local Emergency Planning Committees (LEPCs) and State Emergency Response Commissions (SERCs), are also critical components of the decision process. In addition, decisions to manage hazards are determined by state and federal resources, local resources (including the jurisdiction’s budget), and the local resource allocation priorities.
Once a decision has been made to actively manage one or more hazards, three processes are initiated concurrently. The first is a hazard management planning process that examines mitigation and preparedness strategies. That is, the community must consider whether it is possible to eliminate a risk or reduce it through some emergency management strategy. At the local level, these deliberations involve not just emergency managers but also departments of land use planning, building construction, engineering, public works, public health, and elected officials because mitigation and preparedness actions require significant commitments of resources to reduce community hazard vulnerability. At the same time, the process of judging hazard impact begins, using much of the same technical hazard data to create strategies and acquire resources for response and recovery when a disaster strikes. The local response usually centers on preparations for the mobilization of local emergency services (fire department, EMS, hazardous materials teams, police, transportation and public works departments, and emergency managers) under an agreed upon incident management system (Brunacini, 2001; Kramer & Bahme, 1992). Both response and recovery activities are organized in conjunction with support from external sources, particularly the state and federal government. The purpose of this planning process is to institutionalize emergency response as much as possible while looking at disaster recovery as another path to sustainability or disaster resilience (in addition to mitigation). The third process to be initiated is environmental monitoring for the hazards to be managed. Typically, such monitoring is coupled with a warning system whose activation initiates response actions when disaster impact is imminent. The quality of the warning system depends upon the state of technology associated with the hazards to which the community is exposed and could provide days (in the case of hurricanes or riverine flooding) or minutes (in the case of tornadoes) of forewarning (Sorensen, 2000). The nature of the warning system is also affected by jurisdictional mitigation, preparedness, and response plans. In many cases, hazard monitoring is beyond the technical and financial capability of most communities and assumed by federal agencies and programs. In such cases—tsunamis, for example—the results of the monitoring program are relayed to local jurisdictions. Furthermore, information regarding the state of the warning system (its ability to accurately forecast and detect hazards) is shared with hazard planning systems as a means of informing longer term risk management plans.
The community planning process generates hazard management strategies that incorporate knowledge about hazards derived from many sources, including the scientific community and state and federal agencies. The resulting hazard management strategies can be categorized as hazard mitigation, disaster preparedness, emergency response, and disaster recovery. As will be discussed in greater detail below, mitigation seeks to control the hazard source, prevent the hazard agent from striking developed areas, limiting development in hazard prone areas, or strengthening structures against the hazard agent.
These community hazard management strategies must be individually implemented by households and businesses, or collectively implemented by government agencies acting on behalf of the entire community. The individual strategies only reduce the vulnerability of a single household or business. These generally involve simple measures to mitigate hazards by elevating structures above expected flood heights, developing household or business emergency response plans, and purchasing hazard insurance. The collective strategies are generally complex—and expensive—technological systems that protect entire communities. Thus, they mitigate hazards through community protection works such as dams and levees and prepare for hazard impacts through measures such as installing warning systems and expanding highways to facilitate rapid evacuation.
Collective hazard adjustments are relatively popular because they permit continued development of hazard prone areas, yet do not impose any constraints on individual households or businesses. In addition, their cost is spread over the entire community and often buried in the overall budget. Indeed, the cost is often unknowingly subsidized by taxpayers in other communities. For this reason, these collective hazard adjustments are often called “technological fixes”. By contrast, individual hazard adjustments strategies require changes in households’ and businesses’ land use practices and building construction practices. Such changes require one of three types of motivational tactics—incentives, sanctions, or risk communication. Incentives provide extrinsic rewards for compliance with community policies. That is, they offer positive inducements that add to the inherent positive consequences of a hazard adjustment or offset the inherent negative consequences of that hazard adjustment. Incentives are used to provide immediate extrinsic rewards when the inherent rewards are delayed or when people must incur a short-term cost to obtain a long-term benefit. For example, incentives are used to encourage people to buy flood insurance by subsidizing the premiums. Sanctions provide extrinsic punishments for noncompliance with community policies. That is, they offer negative inducements that add to the inherent negative consequences of a hazard adjustment or offset the inherent positive consequences of that hazard adjustment. Sanctions are used to provide immediate extrinsic punishments when the inherent punishments are delayed or when people incur a short-term benefit that results in a long-term cost. For example, sanctions are used to prevent developers from building in hazard prone areas or using unsafe construction materials and methods. The establishment of incentives and sanctions involves using the political process to adopt a policy and the enforcement of incentives and sanctions requires an effective implementation program (Lindell & Perry, 2004).
By contrast, risk communication seeks to change households’ and businesses’ practices for land use, building construction, and contents protection by pointing out the intrinsic consequences of their behavior. That is, risk communication explains specifically what are the personal risks associated with risk area occupancy and also the hazard adjustments that can be taken to reduce hazard vulnerability.
With this overview, discussion can be turned to the four principal functions or phases of emergency management: hazard mitigation, emergency preparedness, emergency response, and disaster recovery. Much of the development and systematization of this four-fold typology may be traced to the efforts of the NGA’s Emergency Management Project. As this group grappled with what it means to manage emergencies, it generated considerable discussion and some controversy within both the disaster research and emergency management communities. Since being adopted by FEMA, it is now widely accepted as an appropriate model for understanding the activities of emergency management. This scheme consolidates emergency activities into four discrete but interconnected categories distinguished by their time of occurrence in relation to disaster impact. Mitigation and preparedness activities are generally seen as taking place before the impact of any given disaster, whereas response and recovery activities are seen as post-impact measures.
Hazard mitigation
Hazard mitigation activities are directed toward eliminating the causes of a disaster, reducing the likelihood of its occurrence, or limiting the magnitude of its impacts if it does occur. Officially, FEMA defines mitigation as “any action of a long-term, permanent nature that reduces the actual or potential risk of loss of life or property from a hazardous event” (Federal Emergency Management Agency, 1998a, p. 9). This definition is somewhat ambiguous because it encompasses the development of forecast and warning systems, evacuation route systems, and other pre-impact actions that are designed to develop a capability for active response to an imminent threat. Thus, Lindell and Perry (2000) contended the defining characteristic of hazard mitigation was that it provides passive protection at the time of disaster impact, whereas emergency preparedness measures develop the capability to conduct an active response at the time of disaster impact. Since 1995, FEMA has emphasized mitigation as the most effective and cost-efficient strategy for dealing with hazards. Indeed, a recent study by the Multihazard Mitigation Council (2005) concluded investments in hazard mitigation return four dollars in losses averted for every dollar invested. The ways in which mitigation activities can reduce hazard losses can best be understood in terms of a model proposed by Burton, et al. (1993) that contends natural hazards arise from the interaction of natural event systems and human use systems. Thus, the potential human impact of an extreme natural event such as a flood, hurricane, or earthquake can be altered by modifying either the natural event system, or the human use system, or both. In the case of floods, for example, the natural event system can be modified by dams or levees that confine flood water. The human use system can be modified by land use practices that limit development of the flood plain or building construction practices that floodproof structures. Although the amount of control that can be exercised over natural event systems is often limited, technological hazards are inherently susceptible to such controls. Chemical, biological, radiological/nuclear, and explosive/flammable materials can all be produced, stored, and transported in ways that avoid adverse effects to plant workers, local residents and the public-at-large. However, this control can be lost, resulting in releases to the air, or to surface or ground water. It is possible to control the hazard agent by locating the system away from populated areas; designing it with diverse and redundant components or by operating it with smaller quantities of hazardous materials (known as hazmat ), lower temperatures and pressures, safer operations and maintenance procedures, and more effective worker selection, training and supervision). Alternatively, one can control the human use system by preventing residential and commercial development—especially schools and hospitals—near hazardous facilities and major hazmat transportation routes. The choice of whether to mitigate technological hazards by controlling the hazard agent or the human use system depends upon political and economic decisions about the relative costs and benefits of these two types of control. Specific questions include who has control over the hazards, what degree of control is maintained, and what incentives there are for the maintenance of control.
Attempts to mitigate natural hazards, or events over which there is little human control, involve controlling human activities in ways that minimize hazard exposure. Thus, land use practices restricting residential construction in floodplains are important mitigation measures against riverine floods. The Hazard Mitigation and Relocation Act of 1993, for example, allows FEMA to purchase homes and businesses in floodplains and remove these structures from harm’s way. Although moving entire communities involves considerable stress for all concerned, an intense and systematic management process—characterized especially by close coordination among federal, state, and local agencies—can produce successful protection of large numbers of citizens and break the repetitive cycle of “flood-rebuild-flood-rebuild” that is so costly to the nation’s taxpayers (Perry & Lindell, 1997b). Likewise, building code requirements are used to restrict construction to those designs that can better withstand the stresses of hurricane force winds or earthquake shocks.
Disaster Preparedness
Disaster preparedness activities are undertaken to protect human lives and property in conjunction with threats that cannot be controlled by means of mitigation measures or from which only partial protection is achieved. Thus, preparedness activities are based upon the premise that disaster impact will occur and that plans, procedures, and response resources must be established in advance. These are designed not only to support a timely and effective emergency response to the threat of imminent impact, but also to guide the process of disaster recovery. A jurisdiction’s disaster preparedness program needs to be defined in terms of
· What agencies will participate in preparedness and the process by which they will plan,
· What emergency response and disaster recovery actions are feasible for that community,
· How the emergency response and disaster recovery organizations will function and what resources they require, and
· How disaster preparedness will be established and maintained.
Emergency managers can address the first of these questions—what agencies and what will be the process for developing disaster preparedness—by defining an emergency management organization. This requires identifying the emergency management stakeholders in the community and developing a collaborative structure within which they can work effectively. It also requires ensuring an adequate statutory basis for disaster preparedness and administrative support from senior elected and appointed officials.
Emergency managers can address the second question—what are the feasible response and recovery actions—by means of analyses conducted to guide the development of major plan functions. These include, for example, evacuation analyses to assess the population of the risk areas, the number of vehicles that will be taken in evacuation, when people will leave, and what is the capacity of the evacuation route system.
Emergency managers can address the third question—how will the response and recovery organizations function—in the emergency operations plan (EOP), the recovery operations plan (ROP), and their implementing procedures. These documents define which agencies are responsible for each of the functions that must be performed in the emergency response and disaster recovery phases. Some of the generic emergency response functions include emergency assessment, hazard operations, population protection, and incident management (Lindell & Perry, 1992, 1996b). While developing the plans and procedures, emergency managers also need to identify the resources required to implement them. Such resources include facilities (e.g., mobile command posts and emergency operations centers—EOCs), trained personnel (e.g., police, fire, and EMS), equipment (e.g., detection systems such as river gages and chemical sensors, siren systems, pagers, emergency vehicles, and radios), materials and supplies (e.g., traffic barricades, chemical detection kits, and self-contained breathing apparatus), and information (e.g., chemical inventories in hazmat facilities, congregate care facility locations and capacities, and local equipment inventories).
Emergency managers can also address the fourth question—how disaster preparedness will be established and maintained—in EOP and ROP. Sections of these plans should define the methods and schedule for plan maintenance, training, drills, and exercises. Training should always be conducted for emergency responders in fire, police, and EMS. In addition, training is needed for personnel in special facilities such as hospitals, nursing homes, and schools.
Emergency Response
Emergency response activities are conducted during the time period that begins with the detection of the event and ends with the stabilization of the situation following impact. FEMA (1998b, p. 12) indicates the goal of emergency response is “to save lives and property by positioning emergency equipment and supplies; evacuating potential victims; providing food, water, shelter and medical care to those in need; and restoring critical public services”. In many cases, hazard monitoring systems ensure authorities are promptly alerted to disaster onset either by means of systematic forecasts (e.g., hurricanes) or prompt detection (e.g., flash floods detected by stream gages), so there is considerable forewarning and consequently a long period of time to activate the emergency response organization. In other cases, such as earthquakes, pre-impact prediction is usually not available, but prompt assessment of the impact area is feasible within a matter of minutes to hours and can quickly direct emergency response resources to the most severely affected areas.
Some of the more visible response activities undertaken to limit the primary threat include securing the impact area, evacuating threatened areas, conducting search and rescue for the injured, providing emergency medical care, and sheltering evacuees and other victims. Operations mounted to counter secondary threats include fighting urban fires after earthquakes, identifying contaminated water supplies, or other public health threats following flooding, identifying contaminated wildlife or fish in connection with a toxic chemical spill, or preparing for flooding following glacier melt during a volcanic eruption. During the response stage, emergency managers must also continually assess damage and coordinate the arrival of converging equipment and supplies so they can be deployed promptly to those areas with the greatest need.
Emergency response activities are usually accomplished through the efforts of diverse groups—some formally constituted, others volunteer—coordinated through an EOC. Usually, local emergency responders dominate the response period. These almost always include police, firefighters, and EMS personnel, and often include public works and transportation employees. Uncertainty and urgency—less prevalent in mitigation, preparedness, and recovery—are important features of the response period. In the world of disaster response, minutes of delay can cost lives and property, so speed is typically essential. However, speed of response must be balanced with good planning and intelligent assessment to avoid actions that are impulsive and possibly counterproductive. Finally, emergency response actions need to be coordinated with disaster recovery. That is, life and property are priorities, but response actions foreshadow recovery actions. For example, damage assessments are later used to support requests for Presidential Disaster Declarations and debris removal might be concentrated on roadways that are essential for restoring infrastructure. The emergency response phase ends when the situation is stabilized, which means that the risk of loss of life and property has returned to precrisis levels.
Disaster Recovery
Disaster recovery activities begin after disaster impact has been stabilized and extends until the community has been returned to its normal activities. In some cases, the recovery period may extend for a long period of time. The Federal Emergency Management Agency (1995a, p. XX) states “[r]ecovery refers to those non-emergency measures following disaster whose purpose is to return all systems, both formal and informal, to as normal as possible.” The immediate objective of recovery activities is to restore the physical infrastructure of the community—water, sewer, electric power, fuel (e.g., natural gas), telecommunication, and transportation—but the ultimate objective is to return the community’s quality of life to at least the same level as it was before the disaster. Recovery has been defined in terms of short-range (relief and rehabilitation) measures versus long-range (reconstruction) measures. Relief and rehabilitation activities usually include clearance of debris and restoration of access to the impact area, reestablishment of economic (commercial and industrial) activities, restoration of essential government or community services, and provision of an interim system for caring for victims—especially housing, clothing, and food. Reconstruction activities tend to be dominated by the rebuilding of major structures—buildings, roads, bridges, dams, and such—and by efforts to revitalize the area’s economic system. In some communities, leaders view the reconstruction phase as an opportunity to institute plans for change that existed before the disaster or to introduce mitigation measures into reconstruction that would constitute an improvement upon the community’s pre-impact state. Such an approach to reconstruction has been documented after the great Alaska earthquake of 1964 (Anderson, 1969a). After the eruption of Mt. Usu on the northern island of Hokkaido, Japan, local leaders convinced the central government to invest in a wide range of civic improvements aimed at enhancing the local area’s economic viability as a tourist center (Perry & Hirose, 1982).
Finally, it should be noted that the bulk of the resources used in the recovery phase (particularly on reconstruction) are derived from extracommunity sources. In the United States, these sources include private organizations and state governments, but for the most part they come from the federal government. Furthermore, even after James Lee Witt began FEMA’s emphasis on hazard mitigation, most of the money and resources for emergency management continued to be consumed in the recovery phase.
Evaluation of the Emergency Management System
The preceding discussion has examined the four principal functions of the emergency management system—mitigation, preparedness, response, and recovery. In summary, two points should be reiterated here. First, although the distinctions among these four functions are fuzzy (i.e., the transition from one phase to the next is gradual rather than sharp), they are distinctly time phased. Mitigation and preparedness measures take place in advance of any specific disaster impact, whereas response takes place during and recovery occurs after disaster impact. Therefore, practical problems accompany the development of mitigation and preparedness strategies because they must usually be accomplished during periods of normal activity, when environmental threats are not imminent. Historical evidence indicates that it has been difficult to mount efforts to engage in these sorts of activities. Response and recovery take place within the context of a disaster impact—clearly unusual times—and benefit from the operation of an emergency social system as well as from the high level of community cohesiveness that usually emerges in the immediate aftermath (Lindell & Perry, 1992).
The second point is that, in the past, far more resources and emphasis have been allocated to response and recovery activities than to mitigation and preparedness. This is consistent with a cycle, well known to disaster researchers and emergency management professionals, of citizen and governmental interest in disasters. Immediately after impact, the attention of both the public and community officials is riveted upon the physical devastation and social disruption. Considerable resources are made available for shelter, food, clothing, and financial aid to victims, as well as debris clearance and the physical restoration of critical facilities within the community. However, public attention declines significantly as time passes. Because considerable time is required to translate such concern into budget allocations and coherent programs, many preparedness measures—and to an even greater extent mitigation measures—have simply failed to be implemented.
To a certain extent this differential emphasis has been a function of the difficulty citizens and political officials have in maintaining a high level of concern about disasters during times when they seem so remote. To do so requires that both citizens and leaders dwell upon negative events that may or may not occur sometime in the future—a task that is almost universally regarded as unpleasant and thus elicits procrastination. Perhaps equally important in the resource disparity, however, are the limitations posed by the technical state of knowledge regarding various hazards. The state of technology itself imposes limits on the types of mitigation and preparedness activities that can be undertaken. If the location of a potentially catastrophic event cannot be defined in advance, the feasible set of mitigation actions is severely limited. For example, tornado risk is essentially uniform within each local jurisdiction. so land use regulation would achieve little reduction in hazard vulnerability. Furthermore, in the absence of a technology of detection and highly accurate impact predictions, many preparedness measures are not feasible—such as evacuation from unreinforced masonry (e.g., brick) buildings immediately before an earthquake. Thus, in the past, it may have not been possible to devote resources anywhere other than to response and recovery. In the future, as more comprehensive forms of emergency management are implemented, the emphasis must shift toward the development of mitigation and preparedness measures within the limits of existing technology while pursuing research and development designed to advance the state of that technology.


<IP_ADDRESS>.4: Third Wave and Queer Feminist Movements
“We are living in a world for which old forms of activism are not enough and today’s activism is about creating coalitions between communities.”
—Angela Davis, cited by Hernandez and Rehman in Colonize This!
Third wave feminism is, in many ways, a hybrid creature. It is influenced by second wave feminism, Black feminisms, transnational feminisms, Global South feminisms, and queer feminism. This hybridity of third wave activism comes directly out of the experiences of feminists in the late 20th and early 21st centuries who have grown up in a world that supposedly does not need social movements because “equal rights” for racial minorities, sexual minorities, and women have been guaranteed by law in most countries. The gap between law and reality—between the abstract proclamations of states and concrete lived experience—however, reveals the necessity of both old and new forms of activism. In a country where white women are paid only 75.3% of what white men are paid for the same labor (Institute for Women’s Policy Research 2016), where police violence in black communities occurs at much higher rates than in other communities, where 58% of transgender people surveyed experienced mistreatment from police officers in the past year (James et. al 2016), where 40% of homeless youth organizations’ clientele are gay, lesbian, bisexual, or transgender (Durso and Gates 2012), where people of color—on average—make less income and have considerably lower amounts of wealth than white people, and where the military is the most funded institution by the government, feminists have increasingly realized that a coalitional politics that organizes with other groups based on their shared (but differing) experiences of oppression, rather than their specific identity, is absolutely necessary. Thus, Leslie Heywood and Jennifer Drake (1997) argue that a crucial goal for the third wave is “the development of modes of thinking that can come to terms with the multiple, constantly shifting bases of oppression in relation to the multiple, interpenetrating axes of identity, and the creation of a coalitional politics based on these understandings” (Heywood and Drake 1997: 3).
In the 1980s and 1990s, third wave feminists took up activism in a number of forms. Beginning in the mid 1980s, the AIDS Coalition to Unleash Power (ACT UP) began organizing to press an unwilling US government and medical establishment to develop affordable drugs for people with HIV/AIDS.  As discussed at the beginning of this text, queer also described anti-categorical sexualities. The queer turn sought to develop more radical political perspectives and more inclusive sexual cultures and communities, which aimed to welcome and support transgender and gender non-conforming people and people of color. This was motivated by an intersectional critique of the existing hierarchies within sexual liberation movements, which marginalized individuals within already sexually marginalized groups. In this vein, Lisa Duggan (2002) coined the term homonormativity , which describes the normalization and depoliticization of gay men and lesbians through their assimilation into capitalist economic systems and domesticity—individuals who were previously constructed as “other.” These individuals thus gained entrance into social life at the expense and continued marginalization of queers who were non-white, disabled, trans, single or non-monogamous, middle-class, or non-western.   Identity politics refers to organizing politically around the experiences and needs of people who share a particular identity. The move from political association with others who share a particular identity to political association with those who have differing identities, but share similar, but differing experiences of oppression (coalitional politics), can be said to be a defining characteristic of the third wave.
Another defining characteristic of the third wave is the development of new tactics to politicize feminist issues and demands. For instance, ACT UP began to use powerful street theater that brought the death and suffering of people with HIV/AIDS to the streets and to the politicians and pharmaceutical companies that did not seem to care that thousands and thousands of people were dying. They staged die-ins , inflated massive condoms, and occupied politicians’ and pharmaceutical executives’ offices. Their confrontational tactics would be emulated and picked up by anti-globalization activists and the radical Left throughout the 1990s and early 2000s. Queer Nation was formed in 1990 by ACT UP activists, and used the tactics developed by ACT UP in order to challenge homophobic violence and heterosexism in mainstream US society.
Around the same time as ACT UP was beginning to organize in the mid-1980s, sex-positive feminism came into currency among feminist activists and theorists. Amidst what is known now as the “Feminist Sex Wars” of the 1980s, sex-positive feminists argued that sexual liberation, within a sex-positive culture that values consent between partners, would liberate not only women, but also men.   Therefore, a key aspect of queer and feminist subcultures is to create sex-positive spaces and communities that not only valorize sexualities that are often stigmatized in the broader culture, but also place sexual consent at the center of sex-positive spaces and communities. Part of this project of creating sex-positive, feminist and queer spaces is creating media messaging that attempts to both consolidate feminist communities and create knowledge from and for oppressed groups.
In a media-savvy generation, it is not surprising that cultural production is a main avenue of activism taken by contemporary activists. Although some commentators have deemed the third wave to be “post-feminist” or “not feminist” because it often does not utilize the activist forms (e.g., marches, vigils, and policy change) of the second wave movement (Sommers, 1994), the creation of alternative forms of culture in the face of a massive corporate media industry can be understood as quite political. For example, the Riot Grrrl movement, based in the Pacific Northwest of the US in the early 1990s, consisted of do-it-yourself bands predominantly composed of women, the creation of independent record labels, feminist ‘zines, and art.  Feminist news websites and magazines have also become important sources of feminist analysis on current events and issues. Magazines such as Bitch and Ms. , as well as online blog collectives such as Feministing and the Feminist Wire function as alternative sources of feminist knowledge production. If we consider the creation of lives on our own terms and the struggle for autonomy as fundamental feminist acts of resistance, then creating alternative culture on our own terms should be considered a feminist act of resistance as well.
As we have mentioned earlier, feminist activism and theorizing by people outside the US context has broadened the feminist frameworks for analysis and action. In a world characterized by global capitalism, transnational immigration, and a history of colonialism that has still has effects today, transnational feminism is a body of theory and activism that highlights the connections between sexism, racism, classism, and imperialism. In “Under Western Eyes,” an article by transnational feminist theorist Chandra Talpade Mohanty (1991), Mohanty critiques the way in which much feminist activism and theory has been created from a white, North American standpoint that has often exoticized “3rd world” women or ignored the needs and political situations of women in the Global South. Transnational feminists argue that Western feminist projects to “save” women in another region do not actually liberate these women, since this approach constructs the women as passive victims devoid of agency to save themselves. These “saving” projects are especially problematic when they are accompanied by Western military intervention. For instance, in the war on Afghanistan, begun shortly after 9/11 in 2001, U.S. military leaders and George Bush often claimed to be waging the war to “save” Afghani women from their patriarchal and domineering men. This crucially ignores the role of the West—and the US in particular—in supporting Islamic fundamentalist regimes in the 1980s. Furthermore, it positions women in Afghanistan as passive victims in need of Western intervention—in a way strikingly similar to the victimizing rhetoric often used to talk about “victims” of gendered violence (discussed in an earlier section). Therefore, transnational feminists challenge the notion—held by many feminists in the West—that any area of the world is inherently more patriarchal or sexist than the West because of its culture or religion through arguing that we need to understand how Western imperialism, global capitalism, militarism, sexism, and racism have created conditions of inequality for women around the world.
In conclusion, third wave feminism is a vibrant mix of differing activist and theoretical traditions. Third wave feminism’s insistence on grappling with multiple points-of-view, as well as its persistent refusal to be pinned down as representing just one group of people or one perspective, may be its greatest strong point. Similar to how queer activists and theorists have insisted that “queer” is and should be open-ended and never set to mean one thing, third wave feminism’s complexity, nuance, and adaptability become assets in a world marked by rapidly shifting political situations. The third wave’s insistence on coalitional politics as an alternative to identity-based politics is a crucial project in a world that is marked by fluid, multiple, overlapping inequalities.
In conclusion, this unit has developed a relational analysis of feminist social movements, from the first wave to the third wave, while understanding the limitations of categorizing resistance efforts within an oversimplified framework of three distinct “waves.” With such a relational lens, we are better situated to understand how the tactics and activities of one social movement can influence others. This lens also facilitates an understanding of how racialized, gendered, and classed exclusions and privileges lead to the splintering of social movements and social movement organizations. This type of intersectional analysis is at the heart not only of feminist activism but of feminist scholarship. The vibrancy and longevity of feminist movements might even be attributed to this intersectional reflexivity—or, the critique of race, class, and gender dynamics in feminist movements. The emphasis on coalitional politics and making connections between several movements is another crucial contribution of feminist activism and scholarship. In the 21st century, feminist movements confront an array of structures of power: global capitalism, the prison system, war, racism, ableism, heterosexism, and transphobia, among others. What kind of world do we wish to create and live in? What alliances and coalitions will be necessary to challenge these structures of power? How do feminists, queers, people of color, trans people, disabled people, and working-class people go about challenging these structures of power? These are among some of the questions that feminist activists are grappling with now, and their actions point toward a deepening commitment to an intersectional politics of social justice and praxis.


6.4: Exercise, Physical Fitness, and Sports
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Recess and Physical Education: Recess is a time for free play and Physical Education (PE) is a structured program that teaches skills, rules, and games. They’re a big part of physical fitness for school-age children. For many children, PE and recess are the key components in introducing children to sports. After years of schools cutting back on recess and PE programs, there has been a turnaround, prompted by concerns over childhood obesity and the related health issues. Despite these changes, currently, only the state of Oregon and the District of Columbia meet PE guidelines of a minimum of 150 minutes per week of physical activity in elementary school and 225 minutes in middle school (SPARC, 2016).
Organized Sports: Pros and Cons
Middle childhood seems to be a great time to introduce children to organized sports, and in fact, many parents do. Nearly 3 million children play soccer in the United States (United States Youth Soccer, 2012). This activity promises to help children build social skills, improve athletically and learn a sense of competition. However, the emphasis on competition and athletic skill can be counterproductive and lead children to grow tired of the game and want to quit. In many respects, it appears that children's activities are no longer children's activities once adults become involved and approach the games as adults rather than children. The U. S. Soccer Federation recently advised coaches to reduce the amount of drilling engaged in during practice and to allow children to play more freely and to choose their own positions. The hope is that this will build on their love of the game and foster their natural talents.
Sports are important for children. Children’s participation in sports has been linked to:
- Higher levels of satisfaction with family and overall quality of life in children
- Improved physical and emotional development
- Better academic performance
Yet, a study on children’s sports in the United States (Sabo & Veliz, 2008) has found that gender, poverty, location, ethnicity, and disability can limit opportunities to engage in sports. Girls were more likely to have never participated in any type of sport.
This study also found that fathers may not be providing their daughters as much support as they do their sons. While boys rated their fathers as their biggest mentor who taught them the most about sports, girls rated coaches and physical education teachers as their key mentors. Sabo and Veliz also found that children in suburban neighborhoods had a much higher participation in sports than boys and girls living in rural or urban centers. In addition, Caucasian girls and boys participated in organized sports at higher rates than minority children. With a renewed focus, males and females can benefit from all sports and physical activity.27
Welcome to the World of E-Sports
The recent Sport Policy and Research Collaborative (2016) report on the “State of Play” in the United States highlights a disturbing trend. One in four children between the ages of 5 and 16 rate playing computer games with their friends as a form of exercise. In addition, e-sports , which as SPARC writes is about as much a sport as poker, involves children watching other children play video games. Over half of males, and about 20% of females, aged 12-19, say they are fans of e-sports. Play is an important part of childhood and physical activity has been proven to help children develop and grow. Adults and caregivers should look at what children are doing within their day to prioritize the activities that should be focused on.29
Contributors and Attributions
27. Lifespan Development: A Psychological Perspective by Martha Lally and Suzanne Valentine-French is licensed under CC BY-NC-SA 3.0 (modified by Dawn Rymond)
29. Lifespan Development: A Psychological Perspective by Martha Lally and Suzanne Valentine-French is licensed under CC BY-NC-SA 3.0 (modified by Dawn Rymond)


1.4: Roles and Responsibilities
Ensuring workplace safety is the shared responsibility of WorkSafeBC, employers, and employees. All three have different roles to play in ensuring workplace safety is a priority.
WorkSafeBC Responsibilities
WorkSafeBC is a provincial body set up to maintain a safe, healthful working environment at job sites throughout the province. In addition to providing employers and workers with guidance and assistance when they are setting up health and safety programs, WorkSafeBC, has specific workplace responsibilities.
Under the Workers Compensation Act, WorkSafeBC is responsible for:
- Inspecting places of employment
- Investigating accidents and the causes of industrial diseases
- Issuing orders and directions specifying means of preventing injuries and industrial disease
- Assisting and advising employers and workers in developing health and safety programs
- Educating workers about industrial health and safety
- Providing living allowances, rehabilitation, and retraining for workers injured on the job
- Collecting contributions to an accident fund from employers and distributing money from the fund to injured workers
WorkSafeBC is a regulatory body and can order unsafe job sites closed until they are made safe. It is also responsible for issuing fines and penalties to employers as a result of workplace accidents.
The Occupational Health and Safety Regulation (OHS Regulation), [1] contains all the rules, regulations, and responsibilities relating to WorkSafeBC, employers, and workers.
WorkSafeBC dictates that every employer must make a copy of the Regulation readily available at each place of employment so workers can refer to it. This may be done either by including a hard copy version with other safety information that is provided to employees as a part of their training, or by providing instructions on how to access the Regulation online. The Regulation begins with a general explanation of terms, the procedure for notification of injury, and first aid requirements.
Employer’s Responsibilities
The Act lists many, but not all, of the responsibilities of all employers. A few of these responsibilities are noted below. Additional conditions are noted in the OHS Regulation.
The employer must ensure that:
- All work is carried out without undue risk of injury or industrial disease
- Machinery and equipment are capable of safely performing the functions for which they are used
- All permanent and temporary buildings and structures are capable of withstanding any stresses likely to be imposed on them
- All buildings, excavation structures, machinery, equipment, tools, and places of employment are maintained in good condition so workers will not be endangered
- Regular inspections are made to prevent structures, grounds, excavations, tools, equipment, machinery, and work from becoming unsafe
- Any unsafe conditions are corrected without delay
- Each worker is supplied, at no cost, with all protective safety equipment required by WorkSafeBC regulations
- All workers are instructed in the safe performance of their duties
- An accident prevention program is set up
- There is a safe means of entry to and exit from the work area
- Firefighting equipment is provided and maintained
- Workers with physical or mental impairment are not assigned to work where their impairment endangers themselves or others
- No one enters or remains, or is permitted to remain, on the premises of any place of employment while that person’s ability to work is so affected by alcohol, drugs, or other substances as to endanger his or her health or safety, or that of any other person
Employee’s Responsibilities
Workers are responsible for their own safety on the job. This means that you have the right to refuse to do any act or operate any tool, appliance, or equipment when you have reasonable cause to believe that to do so would put you in danger.
It is your responsibility to wear proper clothing for the job site and to use the PPE provided by your employer or required for your job.
As a worker, you should keep the following personal responsibilities in mind:
- You must not remove any safety equipment from machines or equipment. This includes shields from grinders, mixers, etc.
- You must have had adequate instruction about a piece of machinery or equipment before you use it.
- You must make sure that no machine, equipment, or tool is used in a way that would cause injury to someone else.
- You must make sure that there are safe entrances to and exits from the workplace.
- You must make sure that the work area is safe for the movement of workers, equipment, and materials.
- You must wear protective eyewear when using grinders and other equipment that may be hazardous to the eyes.
Health and Safety Committees
The employer is responsible for setting up an accident prevention program. As part of the program, a health and safety committee must be established for any employer with more than 20 full-time employees. Employers with fewer than 20 full-time employees are not required to have a safety committee, but it is an industry best practice to do so.
This committee is required to have at least four members who are experienced in the workplace. The membership of the committee must represent both employers and workers, and the number of employer representatives must never outnumber the number of worker representatives.
It is the committee’s responsibility to help create a safe place to work, recommend actions that will improve the effectiveness of the health and safety program, and promote enforcement of WorkSafeBC regulations.
Contravention of Regulations
The OHS Regulation clearly defines contravention as well as the liability of contravening the Regulation. [2]
- A contravention of this Regulation will be deemed to be a contravention by the employer and will make that employer liable for any penalty prescribed by the Workers Compensation Act .
- A contravention of this Regulation by a supervisor or a worker will be deemed to be a contravention by the supervisor and will make that supervisor liable for any penalty prescribed by the Workers Compensation Act
- A contravention of this Regulation by a worker will make that worker liable for any penalty prescribed by the Workers Compensation Act .
- A contravention of this Regulation by a person working in or contributing to the production of an industry within the scope of the Workers Compensation Act will make that person liable for any penalty prescribed by the Act .
Reporting Accidents
According to the OHS Regulation, an employer must immediately notify WorkSafeBC whenever an accident occurs that:
- Results in serious injury to or the death of a worker
- Involves a major structural failure or collapse of a building, bridge, tower, crane, hoist, temporary construction support system, or excavation
- Involves the major release of a hazardous substance
- Is an incident required by regulation to be reported
Note that “near misses” occur more often than accidents. Near misses are incidents in which there is no visible injury or damage but that could have resulted in serious injury, in death, or property damage. They are generally more reflective of a business’s operating guideline than are actual accidents or injuries, and they should also be reported to WorkSafeBC . [3] Reporting near misses is a good way to prevent their recurrence. They should be seen as a learning opportunity and not as a reason to question the ability of the people involved.
Investigating incidents
Prompt investigation of incidents [4] should be conducted so that other employees will not get injured in the same way. Everyone in the business has a role to play, and you must report accidents and incidents to your supervisor.
According to the Regulation, an employer must immediately undertake an investigation into the cause of any accident or other incident that:
- Is required to be reported under the Act
- Results in injury to a worker requiring medical treatment
- Does not involve injury to a worker, or involves only minor injury not requiring medical treatment, but has a potential for causing serious injury to a worker
- Is an incident required by regulation to be investigated
This list does not apply in the case of a vehicle accident occurring on a public street or highway.
- http://www2.worksafebc.com/Publicati...fetyRegulation ↵
- Worker Compensation Act, Occupational Health and Safety Regulation Section 2.8. http://www.bclaws.ca/Recon/document/...side/296_97_01 ↵
- http://www.worksafebc.com/claims/rep...ry/default.asp ↵
- http://www.worksafebc.com/workers/im...ts/default.asp ↵


3.7: Unnecessary Comma
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When beginning writers are first learning comma rules, they have a tendency to forget that the rules all depend upon the situation. So, when you learn to place a comma before a coordinating conjunction like and , but , or so when you join two independent clauses, you might have an urge to place a comma before and , but , or so every time you use these words. You should avoid this urge!
Just because you need to use commas with coordinating conjunctions sometimes doesn’t mean you’ll use them all the time.
In this example, you don’t need a comma before the but because you aren’t combining two independent clauses. Here is a corrected version of the sentence:
You should also be careful that you aren’t using commas unnecessarily around information that is essential to the sentence. The comma rule is that non-essential information should be set off with commas, but essential information should not.
In this example, for my food is not extra information that should be set off with commas. But, you do need a comma before the so to separate the two independent clauses. Here is a corrected version of the sentence:
For more information on these comma rules, be sure to check out the Comma section in the Punctuation area of Grammar Essentials.


4.2: Classical Theme Types - The Period
A period is one type of theme, like the sentence , common to the Classical style.
The period is generally eight measures long and contains two four-measure phrases, called antecedent and consequent .
The period is characterized by balance and symmetry. Its antecedent phrase is initiated by a basic idea that recurs at the beginning of the consequent phrase. Unlike the sentence, which exhibits a single cadence, the period contains two cadences , a weak one to end the antecedent and a strong one to end the consequent .
Antecedent phrase (mm. 1–4)
Unlike the sentence, which contains a basic idea followed by a repetition, the two measure basic idea that begins the a period’s antecedent is always followed by a two-measure contrasting idea (CI). That contrasting idea supports a cadential progression that ends the antecedent with a weak cadence, either a HC or an IAC.
ANTECEDENT: HAYDN, PIANO TRIO IN C MAJOR, HOB. XV:27, III, MM. 1-4
Note the contrast created between the basic idea and contrasting idea. While the BI ascends, outlining the tonic triad with leaps to each of its members, the CI descends stepwise leading to a weak I:HC. The emphasis on tonic in the melody of the BI is accompanied by a tonic prolongation in the harmony (a variant of the Romanesca schema ):
I V6 VI III
or
T(1 D7p x6 3)
Supporting the CI is an expanded cadential progression:
III IV V 6/5 /V V
or
T3 S(4 [+]) D5
Consequent phrase (mm. 5–8)
Consequent phrases always begin with a restatement of the BI, occasionally varied, and end with a CI. A consequent phrase’s CI often resembles the antecedent’s, but slightly altered to accommodate a stronger cadence. It is also common for a consequent phrase’s CI to be entirely new. While a sentence can close with a number of cadence types, the period’s consequent phrase always ends with a PAC:
ANTECEDENT + CONSEQUENT: HAYDN, PIANO TRIO IN C MAJOR, HOB. XV:27, III, MM. 1-8
In this example, the BI is restated exactly at the beginning of the consequent. The concluding CI is a slight variation of the end of the antecedent, altered here to create a PAC.


11.9: Annuities Due
Annuities Due
An “annuity due” is a type of annuity whose cash flows occur at the start of each period. To illustrate, we will use the example – and chart – from above. Since the timing of the cash flows is different than in an ordinary annuity, the factors (and exponents) are also different. As you fill in the factors and the dollar amounts, draw the appropriate timeline.
Question : What would be the PV and FV for the $100 three-year annuity at 10%?
Timeline
Questions:
- Notice that both PV and FV annuity due factors (and dollars therefore) are larger than the respective ordinary annuity factors.
- The PV of an annuity due is equal to the PV of an ordinary annuity multiplied by one plus the discount rate (1 + R/P) 1 for one period.
- The FV of an annuity due is equal to the FV of an ordinary annuity multiplied by the compound rate for one period. Show this mathematically.