A certain forest covers an area of 3500km^2

Question

A certain forest covers an area of 3500km². Suppose that each year this area decreases by 8.75%. What will the area be after 8 years? Round your answer to the nearest square kilometer.

Answer 1

Note that the area of this certain forest after the first year is

3500-0.0875*3500=(1-0.0875)*3500

=0.9125*3500

Also note that the area of this certain forest after the second year is

0.9125*3500-0.0875*0.9125*3500=(1-0.0875)*0.9125*3500

=0.9125*0.9125*3500

=0.9125^2*3500

Continuing to follow this same line of reasoning then tells us that the area of this certain forest after the eighth year is

0.9125^8*3500=1682.406856,

which rounds to 1682 km².