Posted by **HEENA** on Friday, October 9, 2009 at 11:16am.

If a population consists of ten thousand individuals at time t=0 (P0), and the annual growth rate (excess of births over deaths) is 3% (GR), what will the population be after 1, 15, and a 100 years (n)? Calculate the "doubling time" for this growth rate. Given this growth rate, how long would it take for this population of a hundred thousand individuals to reach 1.92 million? one equation that may be useful is:

Pt=Po * (1+ {GR/100})n

Additionally, using the current world population from the census website, calculate world population in 2100 with growth rates of 2.3% and 0.5% why is this important?

- MATH -
**MathMate**, Friday, October 9, 2009 at 12:22pm
The first part of the question has been answered before. See:

http://www.jiskha.com/display.cgi?id=1254881441

For the second part of the question, it is essentially the same idea. By using the formula

P(2100)=P(2009)*(1+r)^{(2100-2009)}

where

P(t) = projected population in year t

r = rate of growth, for example, 0.023 or 0.005

If you need more help, post any time.

- MATH -
**drwls**, Friday, October 9, 2009 at 12:27pm
Your equation should be

Pt=Po * (1+ {GR/100})^n

The n is an exponent.

Why don't you just apply the formula?

After 100 years,

Pt/Po = (1.03)^100 = 19.2

Note that ratio also equals

1.92 million/100,000

The population doubling time is about 24 years. There is a handy approximate rule of thumb that says

(growth rate, %)*(doubling time, years) = 72

The exact answer is

log2/(log 1.03) = 23.45 years

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