Cumulative growth

[Coritani]

Hi, I've been thinking about this problem for about a week now, but I can't figure it out. The best way to explain it would be to use population growth as an example:

Say the population of a city is 1000. The population grows by 2% annually. What will the population be after 10 years?

Now, I could just go the long way and work out the population year by year (e.g it's 1020 after 1 year, then after the 2nd year it's 1040.4 etc), but there must be a quicker way - a formula or something.

Anyone know?

[lintz]

Chek out this link (http://math.about.com/library/weekly/aa042002a.htm). It uses $ in the example but you can apply that to your question. HTH :D

[Coritani]

Chek out this link (http://math.about.com/library/weekly/aa042002a.htm). It uses $ in the example but you can apply that to your question. HTH :D

Cheers, that was exactly what I was looking for.

Is there a way to find out how long it would take the population to go from 1000 to 2000, at a rate of 5% annual increase? Can I just rearrange the formula to find this out?

[jeroen79]

newpop = oldpop * rate^years

[Rassis]

years = [log(newpop/oldpop)]/[log(1+rate)]

Cheers