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?

In general, please round to one decimal place. But think logically if it is a number of insects, you cannot have half of an insect.

Solution

p(t) = 400 e^.03t

1.standard equation of exponential growth is

P = Po e^(rt)

where , Po is the initial value of insects

P is teh final value

r is the rate of growth

t is the time in days

therefore,

1) initial number of insects = 400

2) population after 15 days = plug t= 15

p(t) = 400 e^.03*15

p(t) = 627 insects

3) when will population reach 600

plug p(t) = 600

p(t) = 400 e^.03t

600 = 400 e^(.03t)

1.5 = e^(.03t)

t = 13.50 days

4) when will population double

plug p(t) = 800

800 = 400 e^.03t

2 = e^(.03t )

t = 23.10 days