Given:
The exponential function is,
[tex]P=20000e^{0.02t}[/tex]The final population is, P = 40000.
The objective is to find the correct expression to calculate the number of tears
t.
Explanation:
Substitute the value of P in the given function.
[tex]\begin{gathered} 40000=20000e^{0.02t} \\ \frac{40000}{20000}=e^{0.02t} \\ 2=e^{0.02t} \end{gathered}[/tex]To solve the exponential function, multiiply ln on both sides of the equation.
[tex]\begin{gathered} \ln (2)=\ln e^{0.02t} \\ \ln (2)=0.02t \end{gathered}[/tex]Solve for t:
On further solving the above equation,
[tex]t=\frac{\ln (2)}{0.02}[/tex]Hence, option (a) is the correct answer.
