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In the year​ 2000, the population of a certain country was 280 280 million with an estimated growth rate of 0.6 0.6​% per year.

a. based on these​ figures, find the doubling time and project the population in 2120 2120.
b. suppose the actual growth rates are just 0.2 percentage points lower and higher than 0.6 0.6​% per year ​( 0.4 0.4​% and 0.8 0.8​%). what are the resulting doubling times and projected 2120 2120 ​population?

User Vonder
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a. If the growth rate is 0.6% per year, it means the population is multiplied by a factor of 1 + 0.6/100 = 1.006 each year. Then the doubling time d (in years) can be found from

... 2 = 1.006^d

... ln(2) = d×ln(1.006)

... d = ln(2)/ln(1.006) ≈ 115.9 . . . years

The population will be multiplied by that factor 120 times in 120 years from 2000 to 2120, so will be

... p = 280×1.006^120 ≈ 574 . . . . million

b. The numbers for the remaining scenarios can be found by replacing 6 with 4 or 8 in the above calculations. Doing that gives you

... 0.4% growth: doubling in 174 years, 2120 population 452 million

... 0.8% growth: doubling in 87 years, 2120 population 728 million

_____

It is convenient to let a calculator or spreadsheet do the repeated calculations.

In the year​ 2000, the population of a certain country was 280 280 million with an-example-1
User Baig
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