Question

Calc !

PLEASEE HELPP!

The size of a certain insect population is given by P(t) = 200e0.01t, where t is
measured in days. At what time will the population equal 1000?

Answer 1

109.861 days

Explanation:

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

Answer 2

Your answer is about t = 621.5 days the population of insect will equal to 1000.

Explanation:

Given:

`P(t)=200e^(0.01t)` and population equal to 1000?

You are trying to find t in number of days when the insect population reaches equal to 1000 so.

`1000=200e^(0.01t)\\\\(1000)/(200)=e^(0.01t) \\\\500=e^(0.01t)\\\\ln(500)=0.01t\\\\t=(ln(500))/(0.01) \\\\t=621.4608098`