Question

The population of a town can be modeled using the formula P = 20,000e^0.02t, where t is the number of years after 2012 and P is the town's population. Which of the following equations can be used to find the number of years after 2012 that the population will double to 40,000?a) t = In2/0.02b) t = In20,000/0.02c) t = log2/0.02d) t = 2/0.02e

Answer 1

Given:

The exponential function is,

`P=20000e^(0.02t)`

The final population is, P = 40000.

The objective is to find the correct expression to calculate the number of tears

t.

Step-by-step explanation:

Substitute the value of P in the given function.

`\begin{gathered} 40000=20000e^(0.02t) \\ (40000)/(20000)=e^(0.02t) \\ 2=e^(0.02t) \end{gathered}`

To solve the exponential function, multiiply ln on both sides of the equation.

`\begin{gathered} \ln (2)=\ln e^(0.02t) \\ \ln (2)=0.02t \end{gathered}`

Solve for t:

On further solving the above equation,

`t=(\ln (2))/(0.02)`

Hence, option (a) is the correct answer.