Question
From the Chapter 8 opener, we have two functions to describe the amount of sulfur dioxide emissions in the United States. For both functions, $x$ is the number of years since 1970 and $y$ (or $f(x)$ or $g(x))$ is the amount of emissions in millions of tons.$$f(x)=-0.59 x+32.38 \text { or } g(x)=-0.0045 x^2-0.37 x+30.89$$Use this for Exercises 69 through 74. See Section 3.6.Find $f(30)$ and describe in words what this means.
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In the United States over the years $1980-2000$, sulfur dioxide emissions due to the burning of fossil fuels can be approximated by the equation $$y=-0.4743 t+24.086$$ where $y$ represents the sulfur dioxide emissions (in millions of tons) for the year $t$, with $t=0$ corresponding to $1980 .$ Source: This equation (and the equation in Exercise 48) were computed using data from the book Vital Signs 1999 Lester Brown et al. (New York: W. W. Norton \& $\mathrm{Co} ., 1999$ ). (a) Use a graphing utility to graph the equation $y=-0.4743 t+24.086$ in the viewing rectangle [0,25,5] by $[0,30,5] .$ According to the graph, sulfur dioxide emissions are decreasing. What piece of information in the equation $y=-0.4743 t+24.086$ tells you this even before looking at the graph? (b) Assuming this equation remains valid, estimate the year in which sulfur dioxide emissions in the United States might fall below 10 million tons per year. (You need to solve the inequality $-0.4743 t+24.086 \leq 10 .)$
Equations and Inequalities
Inequalities
A common air pollutant responsible for acid rain is sulfur dioxide $\left(\mathrm{SO}_{2}\right) .$ Emissions of $\mathrm{SO}_{2}$ during year $x$ are computed by $f(x)$ in the table. Emissions of carbon monoxide (CO) are computed by $g(x)$ Amounts are given in millions of tons. $$\begin{array}{c|c|c|c|c|c}\boldsymbol{x} & 1970 & 1980 & 1990 & 2000 & 2010 \\\hline \boldsymbol{f}(\boldsymbol{x}) & 31.2 & 25.9 & 23.1 & 16.3 & 13.0 \\\hline \boldsymbol{g}(\boldsymbol{x}) & 204.0 &185.4 & 154.2 & 114.5 & 74.3\end{array}$$ (a) Evaluate $(f+g)(2010)$ (b) Interpret $(f+g)(x)$ (c) Make a table for $(f+g)(x)$
Analysis of Graphs of Functions
Operations and Composition
Solve each problem. See Example 9. Worldwide emissions in millions of metric tons of the greenhouse gas carbon dioxide from fossil fuel consumption during the period $1990-2006$ can be modeled by the function defined by $$ f(x)=20,761 e^{0.01882 x} $$ where $x=0$ corresponds to $1990, x=1$ to $1991,$ and so on. Approximate, to the nearest unit, the emissions for each year. (Source: U.S. Department of Energy.) (a) 1990 (b) 1995 (c) 2000 (d) 2006
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