Question

0.08tThe size P of a certain insect population at time t (in days) obeys the function P(t) = 200 ea(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 320?(e) When will the insect population double?

Answer 1

The function P is given by:

$P(t)=200e^{0.08t}$

Substitute t=0 into the formula:

$P(t)=200e^{0.08\cdot0}=200e^0=200$

Therefore, the number of insects at t=0 is 200