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.
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.
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?
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.
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!
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, $\displaystyle P(t)= P_0(2^{1/183})= 0.005464P_0$.