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? Round your answer to the nearest whole number. Enter your answer in the box.

Answer 1

The answer is 8069 insects

P(t) = A * e^(r*t)
P(t) - the insect population at the end of t weeks.
A - the initial number of insects
r - the growth rate
t - number of weeks

P(t) = ?
A = 20
r = 50% = 0.5
t = 12 weeks

P(t) = 20 * e^(0.5*12)
P(t) = 20 * 
P(t) = 20 * e^(0.5*12)
P(t) = 20 * 403.43
P(t) ≈ 8069 insects