Question

The population of the country will be 258 million in

Answer 1

The population, A, is modelled by;

`A=243.9e^(0.003t)`

Where t is the number of years after 2003.

Thus;

`When\text{ }A=258`

The number of years, t, is;

`\begin{gathered} 258=243.9e^(0.003t) \\ \\ \text{ Divide both sides by }243.9; \\ \\ (258)/(243.9)=(243.9e^(0.003t))/(243.9) \\ \\ e^(0.003t)=1.0578 \end{gathered}`

Take the logarithm of both sides of the equation;

`\begin{gathered} \ln(e^(0.003t))=\ln(1.0578) \\ \\ 0.003t=0.0562 \\ \\ \text{ Divide both sides by }0.003 \\ \\ (0.003t)/(0.003)=(0.0562)/(0.003) \\ \\ t\approx19 \end{gathered}`

ANSWER: The population of the country will be 258 millions in 2022