The size P of a certain insect population at time t in days

The size P of a certain insect population at time t (in days) obeys the function

1. What is the initial number of insects (at t=0 days)

2. What is the population after 15 days?

3. When will the insect population reach 600?

4. When will the insect population double?

P(t) = 400e^0.03t

1) intial population : t=0

P(0) = 400

2) after t= 15 days:

P(15) = 400e^(0.03*15)= 400*1.57 = 627.32

3) P(t) = 600 solve for t:

600 = 400e^(0.03t)

3/2 = e^(0.03t)

ln(1.5) = 0.03t

t = 13.5 days

4) Popualtion will double:

800 = 400e^0.03t

t = 23.10 days