We have to calculate when the population will reach 108 millions using the formula for A(t).
We can do it like this:
[tex]\begin{gathered} A(t)=108 \\ 64.5e^{0.02t}=108 \\ e^{0.02t}=\frac{108}{64.5} \\ e^{0.02t}\approx1.674 \\ \ln (e^{0.02t})\approx\ln (1.674) \\ 0.02t\approx\ln (1.674) \\ t\approx\frac{\ln (1.674)}{0.02} \\ t\approx\frac{0.515}{0.02} \\ t\approx26 \end{gathered}[/tex]Answer: it will take 26 years for the population to reach 108 millions.
