Chapter 5.8, Problem 32AE

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 an Insect Population An insect population grows exponentially.

(a) If the population triples in 20 days, and 50 insects are present initially, write an exponential function of the form $P(t)={\text{P}}_0\ast {\text{3}}^{t/n}$ that models the population.

(b) Graph the function using a graphing utility.

(c) What will the population be in 47 days?

(d) When will the population reach 700?

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