Demographics—Immigration and Greenhouse Gases: In his book Bleeding Hearts and Empty Promi...

Demographics—Immigration and Greenhouse Gases: In his book Bleeding Hearts and Empty Promises: A Liberal Rethinks Immigration, Philip Cafaro, associate professor of philosophy at Colorado State University, claims that immigration to the United States has contributed to higher levels of greenhouse gas emissions. (Source: Center for Immigration Studies.) The amount of greenhouse gas emissions annually in the United States from 1990 to 2010 can be modeled by

 f(x) = −3.39x2 + 122.44x + 5977 0 ≤ x ≤ 20

where x represents the number of years since 1990 and f(x) represents the amount of greenhouse gas emissions in millions of metric tons. (Source: Google Public Data.) The number of immigrants to the United States from 1990 to 2010 can be modeled by

 g(x) = −0.03x + 1.42 0 ≤ x ≤ 20

where x represents the number of years since 1990, and g(x) represent the number of immigrants coming to the United States annually in millions. (Source: U.S. Census Bureau.)

(a) Form the function , to measure the number of tons of greenhouse gasses in the United States per immigrant.

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(b) Determine h′(x).

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(c) Evaluate h′(2) and h′(17) and interpret each.

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(d) Do the results in part (c) support the professor’s premise? Explain.