Question

the number of people living in a country is increasing each year exponentially so that the number of people 5 years ago was 4 million. the number of people in five years time is projected to be 6.25 million. what is the present population of the country?

Answer 1

You could attempt doing a log mean.

If your population was growing linearly, you could simply do:

$\frac{(Y_2+Y_1)}{(2)}=Present$

Y2=6.25million, Y1=4million

This would work since you are right in the middle of a straight line.

However, since your population is growing exponentially, you would take a log mean, which would look like this:

$\frac{(Y_2-Y_1)}{ln(Y_2/Y_1)}$

This will give you the middle number with respect to an exponential curve. This would only work because the time difference is 5 years in both directions, so if the time difference was not equal in both directions, you'd have to develop an exponential equation that would fit your data.