Question

A hot, wet summer is causing a mosquito population explosion in a lake resort area. The number of mosquitos is increasing at an estimated rate of n(t) = 1900 + 10e^0.5t per week (where t is measured in weeks). By how much does the mosquito population increase between the fifth and ninth weeks of summer? (Round your answer to three decimal places.)
______mosquitos

Please show all work, step by step, line by line.

Please justify each step so that I can learn it.

Please box final answer.

Thank you!

Answer 1

Given, estimated rate of number of mosquitos is increasing = n(t) = 1900 + 10*e(0.5*t)

n(t) = 1900 + 10*e^(t/2)

then, the mosquito population increase between the fifth and ninth weeks will be,

P = Mosquito population in ninth week(t = 9) - Mosquito population in fifth week(t = 5)

now, integrate this function,

by putting limits,

P =

9156.693