Question

At the beginning of an environmental study, a forest covered an area of 1500km^2. Since then, the area has decreased by 6.3% each year. Let t be the number of years since the start of the study. Let y be the area that the forest covers in km^2. Write an exponential function showing the relationship between y and y.

Answer 1

The correct answer is:

$y=1500(0.937)^t$

Explanation:

An exponential function is of the form

$y=a\times b^x$, where a is the initial population, b is 1 plus the amount of yearly change, and x is the number of years.

For our problem, a, the initial population, is 1500.

The yearly change is 6.3%; 6.3% = 6.3/100 = 0.063.  Since it is decreasing, this is negative; 1+(-0.063) = 0.937.

We use t as the number of years.

This gives us

$y=1500(0.937)^t$