Size of a certain

Question

The size of a certain insect is given by p(t)= 500e .03t, where t is measured in days . What time will the population equal 2000?

Answer 1

Hello Twan,

I assume that the function p(t) that you gave represents the population of the insect in question as a function of time t (not the "size" of an individual insect.) If so, we can solve the problem as follows. Simply set p(t) = 2000, and solve for t.

p(t) = 2000

500e^.03t = 2000.

Dividing each side by 500 gives

e^.03t = 4

Now take the natural logarithm of each side.

Ln(e^.03t) = Ln(4)

Since Ln(e^A) = A for all A, the above equation becomes

.03t = Ln(4)

t = [Ln(4)]/.03

Using a calculator to get the value of Ln(4), we obtain the final answer.

t = 46.21 days (rounded to the second decimal place.)

Hope that helps! Let me know if you need any further explanation.

William