Chapter 5.8, Problem 31AE

Problems 31 and 32 refer to the following discussion: Uninhibited growth can be modeled by exponential functions other than $A(t)={\text{A}}_0{e}^{kt}$. For example, if an initial population $P_0$ requires $n$ units of time to double, then the function models the size of the population at rime $t$, Likewise, a population requiring $n$ units of time to triple can be modeled by $P(t)={\text{P}}_0\ast {\text{3}}^{t/n}$.

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 $25.000$. 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 $80.000$?

(e) Express the model from part(a)in the form $A(t)={\text{A}}_0{e}^{kt}$.