Population Growth RateDate: 9/5/96 at 12:52:58 From: Anonymous Subject: Population Growth Rate If a population increases from 10 million to 300 million in 10,000 years, what is the annual growth rate? Please send us the formula used to solve the equation. Thanks, Charlie Date: 9/5/96 at 13:56:20 From: Doctor Tom Subject: Re: Population Growth Rate Assuming that the population grows at a constant rate (a VERY bad assumption, I might add), then if the rate is r, every year there will be (1+r) times as many individuals in the population. For example, if the growth rate is 1 percent, every year there are 1.01 times as many individuals. So after 2 years, there will be (1+r)*(1+r) times as many, and so on. In 10000 years, there will be (1+r)^10000 ((1+r) multiplied by itself 10000 times) times as many individuals. So the equation to solve is this: 10000000*(1+r)^10000 = 300000000 or, dividing by 10 million: (1+r)^10000 = 30 Take logarithms of both sides: 10000*log(1+r) = log(30) I'll use log base 10 (it doesn't matter): 10000*log(1+r) = 1.47712125472 or log(1+r) = .000147712125472 or, taking anti-logs: 1+r = 1.00034017759 So the average annual growth rate is .034 percent -- 34 thousandths of a percent -- very tiny. -Doctor Tom, The Math Forum Check out our web site! http://mathforum.org/dr.math/ |
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