A population of insects in a greenhouse follows with insects

MATHEMATICS · Multi-part · AP · Calculus AB · Differential Equations · Differential Equations

Problem

A population of insects in a greenhouse follows

\dfrac{dP}{dt}=kP

with

P(0)=150

insects. After 3 days the population has grown to 240 insects. (a) Determine the exact value of

k

in units of

\text{day}^{-1}

. (b) Compute the relative growth rate

\dfrac{1}{P}\dfrac{dP}{dt}

, expressed as a percentage per day, when

t=6

days. (c) The greenhouse manager wants the instantaneous growth rate to reach 100 insects per day. At what time

t

(in days) will this occur? Justify your result algebraically.