Question

A certin forest covers an area of 2700km^2. Suppose that each year this area decreases by 3%. What will be the area after 15 years?Use a calculator and round your answer to the nearest square kilometer.

Answer 1

Step-by-step explanation:

The decrease can be found with this equation:

`A=A_0(1-r)^t`

A0 is the initial area covered by the forest. r is the annual rate at which this area decreases. t is the time in years and A is the area after t years.

In this problem we have:

• A0 = 2700km²

,

• r = 3% = 0.03

,

• t = 15 years

`\begin{gathered} A=2700(1-0.03)^(15) \\ A=2700\cdot0.97^(15) \\ A\approx2700\cdot0.633 \\ A\approx1709.778 \end{gathered}`

Answer:

Rounded to the nearest square kilometer, the area after 15 years is 1710 km²