Chapter 9.5, Problem 54E

Emissions The table shows data for sulfur dioxide emissions from electricity generation (in millions of short tons) for selected years from 2000 and projected to 2035. These data can be modeled by the function

$E\left(x\right)=\left(0.001x-0.062\right)\left(-0.18x^2+8.2x-200\right)$ where x is the number of years past 2000.

(a) Find the function that models the rate of change of these emissions.

(b) Find and interpret $E\text{'}\left(20\right).$

Year	Short Tons (in millions)
2000	11.4
2005	10.2
2008	7.6
2015	4.7
2020	4.2
2025	3.8
2030	3.7
2035	3.8

Source: U.S. Department of Energy