Exponential Growth

A friend is having some trouble studying for her repeats, a lack of notes on certain topics doesn't help.

Having trouble working through this question

Q1
The population of a country is initially 12 million and grows exponentially and by 2.5% per year.
(a)
What will the size of the population be after 7 years?

The formula I have been using is y = a*b^t
What I have gotten from it

y = 12*(1 + 0.025)^7
y = 12*(1.025)^7
y = 12*1.188685753668212890625
y = 14.2642290440185546875

So 14.26 million years is the answer, yet the answer given with the question is 14.29 million years.

Am I going wrong somewhere, or should I be using a different formula?

Cheers for any help.

bnt

Not 14.26.million years - 14.26 million people!
I think your answer is right, the difference could be a rounding error somewhere along the line ...

Yes yes, people, not years
Yea, I was thinking it must be something like that, but couldn't really get close when adjusting the figures.

Cheers.

MathsManiac

I agree that you are right. It might be reasonable to round to the nearest person once decimal values of people start to kick in in year 3, but even if you do that, your answer is still 14.26 million, (correct to nearest 10,000).

Browney7

Would it not be e^(7*.025)*12 million?

MathsManiac

Well that would give the answer quoted, but would not be correct given the way the question is phrased, as it would not then be correct to state that the population was growing by 2.5% per year.

(The population would then be growing at 2.5315... % per year.)

Supplemantal info:
To use that method correctly, you would have to first convert the annual growth rate into a continuous growth rate = ln(1.025) = 0.0246926...
This would then give the same answer of 14.26 million.