Question

A certain forest covers an area of 4700 km². Suppose that each year this area decreases by 7.5%. What will the area be after 8 years?

Answer 1

To solve this, we will use the formula

`A=A_1(1-\frac{r}{100^{}})^t`

Where

`\begin{gathered} A=\text{ area of the land after 8 years = ?} \\ A_1=\text{ former area of the land = }4700km^(2) \\ r\text{ = percent decrease = }7.5\text{ percent } \\ t\text{ = time in years = 8 years } \end{gathered}`

Substituting the values we have

`\begin{gathered} A=A_1(1-\frac{r}{100^{}})^t \\ A=4700_{}(1-\frac{7.5}{100^{}})^8 \\ A=4700(1-0.075)^8 \\ A=4700(0.925)^8 \\ A=4700*0.53596183 \\ A=2519.020604 \end{gathered}`

Hence the answer is 2519 km² to the nearest square-kilometers