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.

Question

Mathematics

Pitts

30 August, 20:09

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.

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Taliyah Black · 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