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

Marcellus

Mathematics

8 November, 03:52

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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Rodolfo Randall · 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