# Thread: Monthly growth rate with only double time given (exponential)

1. ## Monthly growth rate with only double time given (exponential)

I have a question. I am not looking for the answer just the help to figure it out.

Question is:

"A towns population has doubled after 15 years, 3 months. what is monthly growth rate?"

Any help is appreciated.

2. ## Re: Monthly growth rate with only double time given (exponential)

Hi, robellard. You're right in your heading that it will involve exponentials; logarithms might also be useful too. Do you have any guess as to what the equation you should start with would be?

3. ## Re: Monthly growth rate with only double time given (exponential)

Well the section is focused on geometric sequences, and one formula they give for another problem is:

tn = 26235 * 1.009^(n-1)

I used logarithms to figure out the problem previous to this which is :

"How long would it take for population of focus C (26235 - numbers above) to double.

I am pretty sure it is to include logarithms as well, but I am unsure just how.

4. ## Re: Monthly growth rate with only double time given (exponential)

You're right. To solve the previous problem logarithms would be used. I would look at the current problem in a way similar to the previous problem. Basically in the previous problem you knew the rate, but not the time and so you had something like

$\displaystyle 2=(1.009)^{t}$,

where you needed to solve for $\displaystyle t$. In this case you have a similar situation, only now you know $\displaystyle t=183$ and it's the rate you need to determine. Does that help give you a place to jump off from? Good luck!

5. ## Re: Monthly growth rate with only double time given (exponential)

I Would have done it as $\displaystyle P(t)= P_0(2^{t/183})$ where t is in months. You should be able to see why- if t= 183= 15*12+ 3 $\displaystyle P(183)= P_0(2^1)= 2P_0$. If t= 1 month, $\displaystyle P(t)= P_0(2^{1/183})= 0.005464P_0$.