Respuesta :
Step 1
Given;
[tex]\begin{gathered} \text{Area the forest covers=4500km}^2 \\ \text{The area decreases by 4.5\% yearly} \end{gathered}[/tex]Required; To find area after 12 years
Step 2
State the formula for the population decrease
[tex]P=P_0(1-r)^t[/tex]where;
[tex]\begin{gathered} P_0=4500\operatorname{km} \\ r=\frac{4.5}{100}=0.045 \\ t=12 \\ P=\text{ Area after a given period of time in the case 12 years} \end{gathered}[/tex]Step 3
Find the area after 12 years
[tex]\begin{gathered} P=4500(1-0.045)^{12} \\ P=4500(0.955)^{12} \\ P=2589.720966 \\ P\approx2589.72\operatorname{km}^2\text{ } \end{gathered}[/tex]Hence, the area the forest will cover after 12 years approximately to decimal places will be = $2589.72 km²
