The size of a certain insect population is given by P(t)=500e^.01t, where t is measured in days.

Question

a) How many insects were present initially?

b) Give a differential equation satisfied by P(t).

c) At what time will the population double?

d) At what time will the population equal 1500?

 

Answer 1

a) initial population means  when t=0, p(0)=500

b) dP/dt=5e^.01t

c)500e^.01t =1000 (divide both sides of eq by 500)

   e^.01t _{=2  (take natural log of both sides)}

ln( e^.01t)=ln(2)

.01t= ln(2) (divide both sides of the eq by .01)

t= ln(2)/.01 

t=69.315 days

 

d) 500e^.01t=1500

 

(repeat steps in (c) above and you will get)

t=ln(3)/.01

t=109.861 days