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Applying Exponential Equations (Finance, Population)
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As long as the birth rate of a population exceeds the death rate, the population size will continue to increase. At a steady, positive per capita growth rate, the population will add a larger number of indi- viduals with each generation. So, a population can increase rapidly with even a small growth rate. A pattern of increase in number due to a steady growth rate is called exponential growth. The observa- tion that populations can grow in this pattern is called the exponential (EKS-poh-NEN-shuhl) model of population growth. One way to understand the exponential model is to study a graph of population size over time. A graph of exponential growth makes the characteristic J-shaped curve shown in Figure 19-6. With expo- nential growth, population size grows slowly when it is small, but growth speeds up as individuals join the population. The exponen- tial model leads us to predict that the population size will increase indefinitely and by a greater number with each time period. Applying the Exponential Model A scientific model is useful if it helps to predict or explain pat- terns that can be observed in reality. Indeed, the exponential model matches observed patterns of growth of real populations, but only under certain conditions and for limited periods of time. For example, a population of microorganisms can grow exponen- tially if provided with an abundance of food and space and if waste is removed. Figure 19-7 shows the growth of bacteria in a laboratory. However, the exponential model does not apply to most popu- lations. In natural environments, populations cannot grow indefi- nitely because the resources they depend on become scarce and harmful wastes accumulate. Any factor, such as space, that restrains the growth of a population is called a limiting factor. All populations are ultimately limited by their environment.SPECIES INTERACTIONS Just as populations contain interacting members of a single species, communities contain interacting populations of many species. Many species have specific types of interactions with other species. This chapter introduces the five major types of interactions among species: predation, competition, parasitism, mutualism, and commensalism. These categories are based on whether each species causes any benefit or harm to the other species in a given relationship. PREDATION In predation (pree-DAY-shuhn), an individual of one species, called the predator, eats all or part of an individual of another species, called the prey. Predation is a powerful force in a community. The relationship between predator and prey influences the size of each population and affects where and how each species lives. Examples of predators include carnivores—predators that eat ani- mals—and herbivores—predators that eat plants. Many types of organisms can act as predators or prey. All heterotrophs are either predators or parasites or both. Predator Adaptations Natural selection favors the evolution of predator adaptations for finding, capturing, and consuming prey. For example, rattlesnakes have an acute sense of smell and have heat-sensitive pits located below each nostril. These pits enable a rattlesnake to detect warm- bodied prey, even in the dark. Many snakes use venom to disable or kill their prey. A venomous rat- tlesnake is shown in Figure 20-1. Other predator adaptations include the sticky webs of spiders, the flesh-cutting teeth of wolves and coyotes, the speed of cheetahs, and the striped pat- tern of a tiger’s coat, which provides camouflage in a grassland habitat. Many herbivores have mouthparts suited to cutting and chewing tough vegetation. A predator’s survival depends on its ability to capture food, but a prey’s survival depends on its ability to avoid being captured. Therefore, natural selection also favors adaptations in prey that allow the prey to escape, avoid, or otherwise ward offApplying the new 'ay' spellings, including 'a', 'eigh' and 'ey'Applying the spellings 'oo', 'ew' and 'u-e' in familiar wordsApplying the spellings ‘ay', ‘ai' and ‘a-e' in familiar wordsApplying the underlying structure of multiplication and division of surdsApplying the spellings 'oa', 'ow' and 'o-e' in familiar wordsApplying the suffix -icApplying the new 'oa' spellings, including 'o' and 'oe'