a certain forest covers an area of 3600 km^2. suppose that each year this area decreases by 8.75%. what will the area be after 15 years

Answer 1

Hi Skylar,

Given the area of 3600, to decrease it by 8.75%, we subtract .0875 · 3600 and get

3600 - .0875 · 3600 = 3600 · (1 - .0875)

(after factoring out 3600) so this is the size of the forest after 1 year. To decrease again by 8.75% (so after 2 years) we do the same thing, again multiplying by the factor (1 - .0875), so we get

3600 · (1 - .0875) · (1 - .0875) = 3600 · (1 - .0875)²

after 3 years it will be

3600 · (1 - .0875)³.

To get the result after 15 years, you just make the exponent 15.

I hope that helps!