130. Population of Mexico. In 2006 the population of Mexico was 107.4 million. I

Question

130. Population of Mexico. In 2006 the population of Mexico was 107.4 million. If Mexico’s population continues to grow at an annual rate of 1.43%, then the population in 2028 will be 107.4(1.0143)14 million.

a) Find the predicted population in 2020 to the nearest tenth of a million people.

b) Use the result of Exercise 129 to determine whether the United States or Mexico will have the greater increase in population between 2006 and 2020.

129. Population of the United States. In 2006 the population of the United States was 300.2 million (U.S. Census Bureau, www.census.gov). If the population continues to grow at an annual rate of 1.05%, then the population in the year 2020 will be 300.2(1.0105)14 million.

a) Evaluate the expression to find the predicted population in 2020 to the nearest tenth of a million people.

b) Use the accompanying graph to estimate the year in which the population will reach 400 million people.

Explanation / Answer

129) a) 300.2(1.0105)^14=347.5 million b) 300.2(1.0105)^x=400 --> 1.0105^x=400/300.2 --> xln(1.0105)=ln(400/300.2) --> x=ln(400/300.2)/ln(1.0105)=27.5 years 130) a)107.4(1.0143)^14=131.0 million b) population growth of Mexico over 14 years=1.0143^14=1.2199 population growth of USA over 14 years=1.0105^14=1.1575 --> population growth of Mexico is greater than that of the US

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