Question

CorrectIf the population of a small town satisfies the exponential model A = Aoe^0.015t, where is measured in years, how long will it take for the town's population to increasefrom 7,300 to 14,600? Round your answer to two decimal places.

Answer 1

ANSWER :

The answer is 46.21 years

EXPLANATION :

From the problem, we have the growth function :

$A=A_oe^{0.015t}$

Solve for t when Ao = 7,300 and A = 14,600

$\begin{gathered} 14600=7300e^{0.015t} \\ \frac{14600}{7300}=e^{0.015t} \\ 2=e^{0.015t} \end{gathered}$

Take ln of both sides :

$\begin{gathered} \ln(2)=\ln(e^{0.015t}) \\ \text{ Note that ln \lparen e\textasciicircum x\rparen is the same as x} \\ \text{ That will be :} \\ \ln(2)=0.015t \\ t=\frac{\ln(2)}{0.015} \\ t=46.21 \end{gathered}$