Question

A population of insects increases at a rate of 250 + 16t +0.3t^2 insects per day. Find the insect population after 3 days, assuming that there are 40 insects at t=0.

Answer 1

d(Insects)/dt = 250 + 16t + .3t^2

so Insects = 250t + 8t^2 + .1t^3 + c
when t=0, Insects = 40, so c = 40

Insects = 250t + 8t^2 + .1t^3 + 40

when t = 3
Insects = 750 + 72 + 2.7 + 40
= appr 865