Question

A certain forest covers an area of 1900 km^2. Suppose that each year this area decreases by 4%. What will the area be after 13 years?

Answer 1

The area of the forest after 13 years is 1,11758km^2

Step-by-step explanation

Given that;

`\begin{gathered} \text{ The original area of forest is 1900km}^2 \\ \text{ The percentage decrease is 4\%} \\ \text{ time is 13 years} \end{gathered}`

Follow the steps below to find the area of the forest after 13 years

Since the size of the forest decreases every year by 4%, then apply the below formula

`\text{ A = A}_{o\text{ }}(1\text{ - r\rparen}^t`

Where

A is the area of the forest after some years

Ao is the original area of the forest

r is the interest rate

t is the time

`\begin{gathered} \text{ A = 1900 \lparen 1 - }(4)/(100))^(13) \\ \\ \text{ A = 1900 \lparen1 - 0.04\rparen}^(13) \\ \text{ A = 1900 \lparen0.96\rparen}^(13) \\ \text{ A = 1900 }*\text{ 0.5882} \\ \text{ A = 1,117.58km}^2 \end{gathered}`

Therefore, the area of the forest after 13 years is 1,11758km^2