solve the problem

Question

The size P of a certain insect population at time t​ (in days) obeys the function P(t)=500e^0.09t.

​(a) Determine the number of insects at

t=0

days.

​(b) What is the growth rate of the insect​ population?

​(c) What is the population after 10​ days?

​(d) When will the insect population reach 850?

​(e) When will the insect population​ double?

Answer 1

a) 500

b) 9%

c) after 10 days P = 500e^.9 = about 1,229.8 = about 1230

d) 850 = 500e^.09t solve for t,

ln(850/500) = .09t

t = (ln1.7)/.09 = about 5.81 days when population reaches 850

e) doubling time is when 2 = e^.09t

and t = (ln2)/.09 = about 7.7 days