Question

If 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 5,450 to 10,355? Round your answer to two decimal placesAnswer

Answer 1

The answer is 42.79 years

EXPLANATION :

From the problem, we have the function :

`A=A_oe^(0.015t)`

Solve for the value of t when A = 10,355 and Ao = 5,450

That will be :

`\begin{gathered} 10355=5450e^(0.015t) \\ (10355)/(5450)=e^(0.015t) \\ 1.9=e^(0.015t) \\ \text{ Take the ln of both sides :} \\ \ln(1.9)=\ln(e^(0.015t)) \\ \ln(1.9)=0.015t \\ t=(\ln(1.9))/(0.15) \\ t=42.79 \end{gathered}`