The population of a city is growing at an average rate of 3% per year in 1990 the population was 45 000.
determine the year which the population will have doubled.

This is an exponential growth/decay problem...

F=Ir^t, F=final value, I=initial value, r=rate, t=time, in this case:

F=I(1.03)^t  and they just want to know when F=2I so

2=1.03^t  take natural log of both sides...

ln2=t*ln1.03

t=ln2/(ln1.03)

t≈23.45

So it will take approximately 23.45 years for the population to double..

1990+23.45=2013.45

So during the year of 2013 the population will have double from its 1990 level.