Question

A local animal rescue has 20 people that help foster pets while they are

waiting on finding their homes. They expect to gain two additional people
willing to foster animals each month. The amount of animals in need of
homes in the community is currently 10 and growing at a rate of 15% per
month. When will the amount of homeless pets surpass the amount of foster
homes available?

A) Write the two functions that represent this situation.

B) Create a table of values for x=0 to x=13.

C) Approximate the solution(s). Why is this the approximate solution?

D) Using graph paper (and the table of values), sketch the situation to
show the exact solution.

Answer 1

A) Let f(x) represent the number of foster homes available after x months, and let g(x) represent the number of homeless pets after x months.

f(x) = 20 + 2x (since 2 additional people are expected to foster each month)

g(x) = 10(1.15)^x (since the number of homeless pets is growing at a rate of 15% per month)