Question

The exponential model A = 64.5e 0.02t describes the population, A, of a country in millions, t years after 2003. Use the model to determThe population of the country will be 108 million in(Round to the nearest year as needed.)

Answer 1

We have to calculate when the population will reach 108 millions using the formula for A(t).

We can do it like this:

`\begin{gathered} A(t)=108 \\ 64.5e^(0.02t)=108 \\ e^(0.02t)=(108)/(64.5) \\ e^(0.02t)\approx1.674 \\ \ln (e^(0.02t))\approx\ln (1.674) \\ 0.02t\approx\ln (1.674) \\ t\approx(\ln (1.674))/(0.02) \\ t\approx(0.515)/(0.02) \\ t\approx26 \end{gathered}`

Answer: it will take 26 years for the population to reach 108 millions.