a certain forest covers an area of 4500 km^2. suppose that each year this area decreases by 8.75%. what will it be after 10 years?

Answer 1

This is an exponential type function because the area is changing by a percentage and that percentage decrease affects the next percentage decrease. This is akin to a savings account that grows by a percentage. The balance keeps increasing and the interest is calculated on the balance that is continually increasing so each interest payment is bigger than the last.

To write an exponential equation, use the form:

(next value) = (initial value)*[1 +/- (interest rate written as a decimal)]^time

Note that I used a +/- , that would be + when the element is increasing (such as population growth or savings accounts) or it would be - when things are decreasing, such as in this case.

So, in your case, we would could let A = the Area a forest covers and t be time in years. Then we would have:

A = 4500(1 - 0.0875)^t

Which could also be written as: A = 4500(0.9125)^t

You could also write this in function notation as A(t) = 4500(0.9125)^t

To determine the area in 10 years, just plug in 10, so:

A(10) = 4500(0.9125)¹⁰ = 1801.11 km²