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

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) \\ (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=(\ln(2))/(0.015) \\ t=46.21 \end{gathered}`