Solution:
The population, A, is modelled by;
[tex]A=243.9e^{0.003t}[/tex]
Where t is the number of years after 2003.
Thus;
[tex]When\text{ }A=258[/tex]
The number of years, t, is;
[tex]\begin{gathered} 258=243.9e^{0.003t} \\ \\ \text{ Divide both sides by }243.9; \\ \\ \frac{258}{243.9}=\frac{243.9e^{0.003t}}{243.9} \\ \\ e^{0.003t}=1.0578 \end{gathered}[/tex]
Take the logarithm of both sides of the equation;
[tex]\begin{gathered} \ln(e^{0.003t})=\ln(1.0578) \\ \\ 0.003t=0.0562 \\ \\ \text{ Divide both sides by }0.003 \\ \\ \frac{0.003t}{0.003}=\frac{0.0562}{0.003} \\ \\ t\approx19 \end{gathered}[/tex]
ANSWER: The population of the country will be 258 millions in 2022
