Continuous Exponential Model
It's an equation that models the growth of a certain variable in time. If P(t) is the number of insects in a colony at a time t, and Po is the initial number of insects of the colony, then the model can be written as:

Where k is the growth rate.
We are given the model equation:

Where the time is in weeks.
A. This corresponds to an original number of insects of Po = 1840
B. The rate of increase can also be determined with the equation. k = 0.145. This corresponds to a rate of 14.5% each week.
C. Now we find the number of insects for t = 16:

It's expected to be 18723 insects in the colony after 16 weeks.
D. For the colony to have 12000 insects, we need to solve the equation:


Dividing by 1840:

Applying logs on each side:

Dividing by 0.145:

Calculating:
t ≈ 13 weeks
It will take approximately 13 weeks for the population to reach 12000