Question

There are 50 tree frogs in the botanical gardens at t = 0. The population increases exponentially by 20% per year.

(A) Write an equation that models the problem

(B) about how many tree frogs will there be when t=3?

(C) about how many years will it take until the tree frog population is 200?

(D) what was the tree frog population at t = -1?

Answer 1

A)

f(t) = 50 * 1.2^t

B)

f(3) = 50 * 1.2^3 = 86.4 tree frogs

C)

f(t) = 50 * 1.2^t = 200 --> t = LN(200/50)/LN(1.2) = 7.604 years

D)

f(-1) = 50 * 1.2^(-1) = 41.67 tree frogs