Question

The size P of a certain insect population at time t(in days) obeys the function in p(t)=500e^0.02t
b. What is the growth rate of insect population?

c. What is the population after 10 days?

Answer 1

The growth rate I'd have to look up again to make sure I'm right, the population after 10 days is going to be an ugly number--just plug 10 in for t and you get 500e^0.2.

In general, population problems like this are going to give you an equation P(t) = Pe^(kt) where:
P is your initial population at t = 0
e is the number e
k is your growth "rate" (technically the growth rate is going to be the derivative k*Pe^(kt), but it's been a long time since I took calc 1 and I don't remember the semantics well enough to answer (b) confidently)
t is your variable.

Answer 2

okay thank you ! :)