need help with questions a-e

Question

The size P of a certain insect population at time t​ (in days) obeys the function .P(t)=900e^0.01t.

​(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 1530?

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

Answer 1

a) 900 b) 1% c) 900e^.1 d)

it reaches 1530 when 1530 = 900e^.01t

153/90 = e^.01t

.01t = ln(153/90)

t =100 (ln(153/90) = 53.06 years

e) it double when 2 = e^.01t

t = 100ln2 = about 69.31 years