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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.)

Sagot :

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.

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