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.