Question

5. A wooded area in a state park has a mixture of different types of trees. There are 800 pine trees and 50 oak trees. The number of pine trees is decreasing at a rate of 5% per year. The number of oak trees is increasing at a rate of 15% per year. If these trends continue:
A. Write two functions to model this situation and graph those two functions on the same coordinate grid. Two functions for this model would be:
y = 800(.95)^x
y = 50(1.15)^x
B. During what year in the future will the park have approximately the same number of pine and maple trees?

Answer 1

The functions in part A are correct, we will now use them to solve for part B.
We equate the numbers of the trees in order to find x, which the number of years after which they will be equal.
800(0.95)ˣ = 50(1.15)ˣ
40 = (1.15 / .95)ˣ
Taking log₁₀ on both sides,
log(40) = x*log(1.15/0.95)
x = 19.31 years