The specific numbers did not appear in the problem. The general method is:

Given `(dp)/(dt)=kp` where `k` is a proportionality constant and `p` is the population at time `t` . We know that any function whose rate of change is proportional to the function itself has the following property:

`(dy)/(dx)=ky=> y=Ce^(kt)` with k the proportionality constant and C a constant.

**Thus we have `p=Ce^(kt)` as the population function. You will take the two data points (the population at two different times) to solve for the two unknowns C and k using substitution.**

Then with that function you can evaluate at any other time t.

In order to find when the population triples, you will solve for t given a known p.

## We’ll help your grades soar

Start your 48-hour free trial and unlock all the summaries, Q&A, and analyses you need to get better grades now.

- 30,000+ book summaries
- 20% study tools discount
- Ad-free content
- PDF downloads
- 300,000+ answers
- 5-star customer support

Already a member? Log in here.

Are you a teacher? Sign up now