Problems 31 and 32 refer to the following discussion: Uninhibited growth can be modeled by exponential functions other than . For example, if an initial population requires units of time to double, then the function models the size of the population at rime , Likewise, a population requiring units of time to triple can be modeled by .
Growth of a Human Population The population of a town is growing exponentially.
(a) If its population doubled in size over an 8-year period and the current population is . write an exponential function of the form that models the population.
(b) Graph the function using a graphing utility.
(c) What will the population be in 3 years?
(d) When will the population reach ?
(e) Express the model from part(a)in the form .
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Precalculus
- Use a graphing calculator to solve each problem. In Example 4, suppose that a birth control program changed the formula for poulation growth to Pt=1000e0.01t. How long will the food supply be adequate? EXAMPLE 4 Using a Graphing Calculator to Solve a popuiation Problem Suppose that a country with a population of 1000 people is growing exponentially according to the population function Pt=1000e0.02t Where t in years. Furthermore, assume that the food supply, measured in adequate food per day per person, is growing linearly according to the function fx=30.625x+2000 In how many years will the population outstrip the food supply?arrow_forwardSuppose that the initial size of a population is n0 and the population grows exponentially. Let n(t) be the size of the population at time t. (a) Write a formula for n(t) in terms of the doubling time a. (b) Write a formula for n(t) in terms of the relative growth rate r.arrow_forwardTo the nearest whole number, what is the initial value of a population modeled by the logistic equation P(t)=1751+6.995e0.68t ? What is the carrying capacity?arrow_forward
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