In 2010, the 2009 populations and projected population rates were released for R

Question

In 2010, the 2009 populations and projected population rates were released for Russia and Ethiopia. The population of Russia in 2009 was 140.9 million; the population of Ethiopia was 82.8 million. Russia is decreasing in population by approximately 0.4% annually; the population of Ethiopia is growing at 2.6%. Using logs and letting x be the number of years since 2009, answer the following questions. Round both answers to the nearest tenth.

a. How long, at the above rates, will it take for the population of Ethiopia to double?

b. How long, at the above rates, will it take for the population of Russia to reach 125 million?

Explanation / Answer

a) here population of ethiopia in x year after 2009 =82.8*(1.026)x

for population to be double; (1.026)x=2

taking log on both sides

xlog(1.026)=log(2)

x=log(2)/log(1.026) =0.30103/0.01115=27.0046 Years

b) for Russia population to reach 125 million : 125 =140.9*(1-0.004)x

0.996x =125/140.9

taking log and solving

xlog(0.996)=log(0.887)

x=29.87 Years

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