The population of a certain community is known to increase at a rate proportional to the number of people present at time t. If the population has doubled in 5 years, how long will it take to triple?

Step-by-step explanation:

We can write this rate as an ordinary differential equation.

Where a is proportional constant, P the population variable, and t the time.

Integrating each side of the equation.

To find C we need to use the initial condiction, it means evaluae P at t=0.

Now, we use the sentence  the population has doubled in 5 years.

We can find "a" in this condition.

Finally, let's find how long will it take to triple.

I hope it helps you!