Locate an approximate value of an irrational number on a number line (L3)

8.NSO.1.1 Locate an approximate value of an irrational number on a number line (L3)

8.2.B Approximate The Value of an Irrational Number and Locate on a Number Line

Figure 18-11 represents the amount of energy stored as organic material in each trophic level in an ecosystem. The pyramid shape of the diagram indicates the low percentage of energy transfer from one level to the next. On average, 10 percent of the total energy consumed in one trophic level is incor- porated into the organisms in the next. Why is the percentage of energy transfer so low? One reason is that some of the organisms in a trophic level escape being eaten. They eventually die and become food for decomposers, but the energy contained in their bodies does not pass to a higher trophic level. Even when an organism is eaten, some of the molecules in its body will be in a form that the consumer cannot break down and use. For example, a cougar cannot extract energy from the antlers, hooves, and hair of a deer. Also, the energy used by prey for cellu- lar respiration cannot be used by predators to synthesize new bio- mass. Finally, no transformation or transfer of energy is 100 percent efficient. Every time energy is transformed, such as during the reactions of metabolism, some energy is lost as heat. Limitations of Trophic Levels The low rate of energy transfer between trophic levels explains why ecosystems rarely contain more than a few trophic levels. Because only about 10 percent of the energy available at one trophic level is transferred to the next trophic level, there is not enough energy in the top trophic level to support more levels. Organisms at the lowest trophic level are usually much more abundant than organisms at the highest level. In Africa, for exam- ple, you will see about 1,000 zebras, gazelles, and other herbivores for every lion or leopard you see, and there are far more grasses and shrubs than there are herbivores. Higher trophic levels con- tain less energy, so, they can support fewer individuals.A population is a group of organisms that belong to the same species and live in a particular place at the same time. All of the bass living in a pond during a certain period of time make up a pop- ulation because they are isolated in the pond and do not interact with bass living in other ponds. The boundaries of a population may be imposed by a feature of the environment, such as a lake shore, or they can be arbitrarily chosen to simplify a study of the population. The humans shown in Figure 19-1 are part of the pop- ulation of a city. The properties of populations differ from those of individuals. An individual may be born, it may reproduce, or it may die. A population study focuses on a population as a whole—how many individuals are born, how many die, and so on. Population Size A population’s size is the number of individuals that the population contains. Size is a fundamental and important population property but can be difficult to measure directly. If a population is small and composed of immobile organisms, such as plants, its size can be determined simply by counting individuals. Often, though, individ- uals are too abundant, too widespread, or too mobile to be counted easily, and scientists must estimate the number of individuals in the population. Suppose that a scientist wants to know how many oak trees live in a 10 km2 patch of forest. Instead of searching the entire patch of forest and counting all the oak trees, the scientist could count the trees in a smaller section of the forest, such as a 1 km2 area. The scientist could then use this value to estimate the population of the larger area. SECTION 1 OBJECTIVES ● Describe the main properties that scientists measure when they study populations. ● Compare the three general patterns of population dispersion. ● Identify the measurements used to describe changing populations. ● Compare the three general types of survivorship curves. VOCABULARY population population density dispersion birth rate death rate life expectancy age structure survivorship curve FIGURE 19-1 A population can be widely distributed, as Earth’s human population is, or confined to a small area, as species of fish in a lake are. Copyright © by Holt, Rinehart and Winston. All rights reserved. 382 CHAPTER 19 If the small patch contains 25 oaks, an area 10 times larger would likely contain 10 times as many oak trees. A similar kind of sampling technique might be used to estimate the size of the pop- ulation shown in Figure 19-2. To use this kind of estimate, the sci- entist must assume that the distribution of individuals in the entire population is the same as that in the sampled group. Estimates of population size are based on many such assumptions, so all esti- mates have the potential for error. Population Density Population density measures how crowded a population is. This measurement is always expressed as the number of individuals per unit of area or volume. For example, the population density of humans in the United States is about 30 people per square kilome- ter. Table 19-1 shows the population sizes and densities of humans in several countries in 2003. These estimates are calculated for the total land area. Some areas of a country may be sparsely popu- lated, while other areas are very densely populated. Dispersion A third population property is dispersion (di-SPUHR-zhuhn). Dispersion is the spatial distribution of individuals within the popu- lation. In a clumped distribution, individuals are clustered together. In a uniform distribution, individuals are separated by a fairly con- sistent distance. In a random distribution, each individual’s location is independent of the locations of other individuals in the popula- tion. Figure 19-3 illustrates the three possible patterns of dispersion. Clumped distributions often occur when resources such as food or living space are clumped. Clumped distributions may also occur because of a species’ social behavior, such as when animals gather into herds or flocks. Uniform distributions may result from social behavior in which individuals within the same habitat stay as far away from each other as possible. For example, a bird may locate its nest so as to maximize the distance from the nests of other birds. These migrating wildebeests in East Africa are too numerous and mobile to be counted. Scientists must use sampling methods at several locations to monitor changes in the population size of the animals. FIGURE 19-2 TABLE 19-1 Population Size and Density of Some Countries Population size Population density Country (in millions) (in individuals/km2) China 1,289 135 India 1,069 325 United States 292 30 Russia 146 8 Japan 128 337 Mexico 105 54 Kenya 32 54 Australia 20 3 dispersion from the Latin dis-, meaning “out,” and spargere, meaning “to scatter” Word Roots and Origins Copyright © by Holt, Rinehart and Winston. All rights reserved. POPULATIONS 383 The social interactions of birds called gannets, which are shown in Figure 19-3b, result in a uniform distribution. Each gannet chooses a small nesting area on the coast and defends it from other gannets. In this way, each gannet tries to maximize its distance from all of its neighbors, which causes a uniform distribution of individuals. Few populations are truly randomly dispersed. Rather, they show degrees of clumping or uniformity. The dispersion pattern of a population sometimes depends on the scale at which the popu- lation is observed. The gannets shown in Figure 19-3b are uni- formly distributed on a scale of a few meters. However, if the entire island on which the gannets live is observed, the distribution appears clumped because the birds live only near the shore. POPULATION DYNAMICS All populations are dynamic—they change in size and composition over time. To understand these changes, scientists must know more than the population’s size, density, and dispersion. One important measure is the birth rate, the number of births occur- ring in a period of time. In the United States, for example, there are about 4 million births per year. A second important measure is the death rate, or mortality rate, which is the number of deaths in a

How to Stop Avalanchesnow with explosives, or by erecting snow fences. Explosives Explosives are primarily used to prevent avalanches, especially at ski resorts where other methods are often impractical. Maintenance staff from the ski resort travel to potential avalanche areas and areas with steep slopes. First, they measure the depth of the snow and its quality. They want to check for hard, loose, wet or icy snow layers. If an area is considered dangerous, small explosives are fired into the side of the steep terrain. The explosion loosens the top layer of snow, which tumbles harmlessly down the mountainside. But using explosives is costly and dangerous. Some researchers are currently experimenting with the cheaper and safer method of using ultrasonic sound waves that shock the snow into falling, averting an avalanche and saving lives. Snow Fences It is very common to put up snow nets or snow fences. These nylon nets or wooden and steel fences are placed at the top of slopes. They prevent the buildup of snow on the downwind side, thereby lessening the chance of a slab avalanche. Beacons and Radio Devices Fortunately, there are companies that specialize in making rescue beacons. These are small electronic devices that send out a radio signal to search and rescue crews. Most people who venture into the backcountry carry some sort of beacon or GPS device. They can help locate a buried victim up to 80 meters away. However, these beacons and GPS devices only send out a signal if the victim turns it on. Often, the victim is too injured to think clearly and press the 'on button.' If search and rescue crews do not quickly reach the victims, the skiers will not be discovered in time. Surviving an Avalanche If you are ever caught in an avalanche, the chances are slim that you will survive. If you are not killed instantly, you only have a short time (15~35 minutes) before your oxygen runs out. Take off your ski, boots and poles. Use a swimming motion to claw your way to the surface. Often people do not know which way is up or down. The effect of this is disorientation. It is not uncommon for avalanche victims to dig in the wrong direction. With proper precautions, both skiers and ski resorts can avoid the tragedy of an avalanche.

How to Stop Avalanches ToB A major concern of ski resorts is avalanche control. Most avalanches occur outside the boundaries of the regular groomed ski runs. But each year, skiers and trekkers on snowshoes go into these remote areas where most avalanches occur. There are two primary ways to prevent avalanches-by blasting the snow with explosives, or by erecting snow fences. Explosives Explosives are primarily used to prevent avalanches, especially at ski resorts where other methods are often impractical. Maintenance staff from the ski resort travel to potential avalanche areas and areas with steep slopes. First, they measure the depth of the snow and its quality. They want to check for hard, loose, wet or icy snow layers. If an area is considered dangerous, small explosives are fired into the side of the steep terrain. The explosion loosens the top layer of snow, which tumbles harmlessly down the mountainside. But using explosives is costly and dangerous. Some researchers are currently experimenting with the cheaper and safer method of using ultrasonic sound waves that shock the snow into falling, averting an avalanche and saving lives. Snow Fences It is very common to put up snow nets or snow fences. These nylon nets or wooden and steel fences are placed at the top of slopes. They prevent the buildup of snow on the downwind side, thereby lessening the chance of a slab avalanche. Beacons and Radio Devices Fortunately, there are companies that specialize in making rescue beacons. These are small electronic devices that send out a radio signal to search and rescue crews. Most people who venture into the backcountry carry some sort of beacon or GPS device. They can help locate a buried victim up to 80 meters away. However, these beacons and GPS devices only send out a signal if the victim turns it on. Often, the victim is too injured to think clearly and press the 'on button.' If search and rescue crews do not quickly reach the victims, the skiers will not be discovered in time. Surviving an Avalanche If you are ever caught in an avalanche, the chances are slim that you will survive. If you are not killed instantly, you only have a short time (15~35 minutes) before your oxygen runs out. Take off your ski, boots and poles. Use a swimming motion to claw your way to the surface. Often people do not know which way is up or down. The effect of this is disorientation. It is not uncommon for avalanche victims to dig in the wrong direction. With proper precautions, both skiers and ski resorts can avoid the tragedy of an avalanche.

Risky environments occur when there is potential for injury, unsafe practices and the surrounding are considered hazardous or reliable. In a sporting and physical activity context, this can be due to a variety of factors such as: playing surface, isolation, water, unpredictability and equipment. A playing surface is the environment in which physical activity takes place. A playing surface can be dangerous or hazardous when the ground is uneven, wet/slippery and debris is present. This can be risky for participants as it can lead to severe injury and or death. An example of this is when physical activity or sport is called off due to wet weather. This puts participants at risk as its presents the possibility of the participants slipping over and cutting themselves or fracturing/breaking a bone. Isolation occurs when a person, people or event is held far away from first aid or a significant population, which can contribute to a risky environment. Acquiring an injury in an isolated location makes it difficult for help, and assistance may take longer to arrive, further putting yourself at risk. For example, bushwalking by yourself at night, the walker could slip and break an ankle. It may then take a while for aid to locate or reach you, further putting yourself at risk. Also, an isolated location makes it difficult to fully assess potential risks leading to an unsafe location for physical activity. With the example of the ultra- marathon, organisers were not able to fully assess the potential risk of bushfires leading to serious injury for their competition therefore isolation is a significant contributing factor to a risky environment. Water is a factor which influences risks in sport and physical activity. The lack of water can lead to dehydration and other health issues. On the other hand, the presence of water can result in slippery surfaces as well as altered or unknown conditions. This can be seen when an athlete takes part in a triathlon. Water is required to remain hydrated, however it can become hazardous. During the run and bike legs, water or rain can result in slippery surfaces and can therefore be dangerous for participants. In the swim leg, water depth and conditions can be unknown, rough or altered creating danger for participants. Evidently, water is an influential factor of the risks in physical activity and sport. Unpredictability will always play a role in sport and physical activity. Situations will never be completely foreseeable nor will risks be avoidable. The optimum risk identification processes cannot completely eliminate risks, simply reduce them. It is important for sporting associations to establish plans and processes not only to identify risk environments but to manage risks should unpredictable circumstances arise. Equipment is a factor that can contribute to a risky environment. If there is a lack of the correct and required equipment in physical activity, or if the equipment is ill-fitting or faulty, participants are then at risk of getting injured. For example, if a cricket player isn’t wearing a helmet and the cricket ball hits their head, they are at risk of serious head injury or death. Therefore, if proper and suitable equipment is available, participants can partake in physical activity safely without risk of injury.

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