Handout_10_EXPONENTIAL FUNCTIONS

Handout_10_EXPONENTIAL FUNCTIONS - There exists a certain...

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There exists a certain irrational number e = 2.718281828 … , which arises naturally in a variety of mathematical situations (much the same way that the number π appears in the problems related to a circle). Perhaps the most useful exponential functions are f(x) = e x and f(x) = e -x*x (the graphs of these functions resemble the curves in Fig 1a and Fig. 2). Exponential Growth Function . Under normal conditions, growth is described by the function f(t) = y 0 e kt , where f(t) is the amount of quantity present at time t , y 0 is the amount present at time t = 0 , and k is a rate constant that characterizes the rate of growth (at k > 0). If k < 0 , then this function describes the exponential decay . Exponential functions play an important role not only in mathematics, but also in business, economics, biology, physical and social sciences, and other areas of study. For example, if you invest the principal P in your bank, then the compound amount S of this principal the end of n interest periods (years) is given by the formula
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Handout_10_EXPONENTIAL FUNCTIONS - There exists a certain...

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