# "A town doubles its populace in 25 years. If it's far growing exponentially, while will it triple its population? The above is a query in my maths textbook within the subject matter Exponential increase & Decay. i am a piece confused as to how I have to technique this query. We have been taught to use the formula: Q=Ae^kt Where Q is the quantity, A is the initial quantity, k is the growth/decay constant and t is the time. In reference to the question, I don't think I need A so here is the equation I ended up with 2Q=e^25k

A town doubles its populace in 25 years. If it's far growing exponentially, while will it triple its population?
The above is a query in my maths textbook within the subject matter Exponential increase & Decay.
i am a piece confused as to how I have to technique this query.
We have been taught to use the formula:
$Q=A{e}^{kt}$
Where Q is the quantity, A is the initial quantity, k is the growth/decay constant and t is the time.
In reference to the question, I don't think I need A so here is the equation I ended up with:
$2Q={e}^{25k}$
Edit:
I found out that
$k=\frac{\mathrm{ln}2}{25}$
I then let Q=3A and the following is my working:
$3A=A{e}^{25\frac{\mathrm{ln}2}{25}t}$
$3A=A{e}^{\mathrm{ln}2t}$
$3={e}^{\mathrm{ln}2t}$
$3={2}^{t}$
$\mathrm{ln}3=t\mathrm{ln}2$
$t=\frac{\mathrm{ln}3}{\mathrm{ln}2}$
$t=1.6$
I can't figure out what is wrong in my working out.
The provided answer is: 39.6 years
You can still ask an expert for help

## Want to know more about Exponential growth and decay?

• Questions are typically answered in as fast as 30 minutes

Solve your problem for the price of one coffee

• Math expert for every subject
• Pay only if we can solve it

Raven Mosley
Start with $Q=A{e}^{kt}$. If the doubling time is 25 years, this translates to
$2A=A{e}^{25k}.$
You should be able to solve for k and make a go of it now.

potrefilizx
hint: once you restore the A, you may divide the 2 equations to take away A and Q. in an effort to permit you to examine k.