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?

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

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

4.

step-by-step explanation:

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