The bar graph shows the amount, in billions of dollars, thatthe United States government

Chapter 3, Problem 107

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The bar graph shows the amount, in billions of dollars, thatthe United States government spent on human resourcesand total budget outlays for six selected years. (Humanresources include education, health, Medicare, SocialSecurity, and veterans benefits and services.)The function p(x) = 1.75x2 - 15.9x + 160 models theamount, p(x), in billions of dollars, that the United Statesgovernment spent on human resources x years after 1970. Thefunction q(x) = 2.1x2 - 3.5x + 296 models total budgetexpenditures, q(x), in billions of dollars, x years after 1970.a. Use p and q to write a rational function that modelsthe fraction of total budget outlays spent on humanresources x years after 1970.b. Use the data displayed by the bar graph to find thepercentage of federal expenditures spent on humanresources in 2010. Round to the nearest percent.c. Use the rational function from part (a) to find thepercentage of federal expenditures spent on humanresources in 2010. Round to the nearest percent. Doesthis underestimate or overestimate the actual percentthat you found in part (b)? By how much?d. What is the equation of the horizontal asymptoteassociated with the rational function in part (a)? If trendsmodeled by the function continue, what percentage ofthe federal budget will be spent on human resourcesover time? Round to the nearest percent.

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