"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

ubwicanyil5 2022-09-12 Answered
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 k t
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:
2 Q = e 25 k
Edit:
I found out that
k = ln 2 25
I then let Q=3A and the following is my working:
3 A = A e 25 ln 2 25 t
3 A = A e ln 2 t
3 = e ln 2 t
3 = 2 t
ln 3 = t ln 2
t = ln 3 ln 2
t = 1.6
I can't figure out what is wrong in my working out.
The provided answer is: 39.6 years
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Answers (2)

Raven Mosley
Answered 2022-09-13 Author has 14 answers
Start with Q = A e k t . If the doubling time is 25 years, this translates to
2 A = A e 25 k .
You should be able to solve for k and make a go of it now.

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potrefilizx
Answered 2022-09-14 Author has 2 answers
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.

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