Question

A population of insects grows exponentially. Initially, there were 20 insects and the population of the insects grew by 50% every week. Use a function P(t)P(t) that represents the insect population at the end of t weeks. What is the insect population at the end of week 12?

Answer 1

I just took this test, the answer is 2595

Answer 2

P(t) = Po(1 + r)^t; where Po is the initial population = 20. r is the rate = 50% = 0.5 and t is the time = 1 weeks

P(t) = 20(1 + 0.5)^12 = 20(1.5)^12 = 20(129.7) = 2,594.9 ≈ 2,595