Education Expenditure The following chart shows the percentage of the U.S. discretionary budget allocated to education from 2003 to 2009. (t = 3 represents the start of 2003.) Percentage of U.S....

Extracted text: Education Expenditure The following chart shows the percentage of the U.S. discretionary budget allocated to education from 2003 to 2009. (t = 3 represents the start of 2003.) Percentage of U.S. budget on education 7.0 7.0 6.9 6.8 6.5 6.3 6.2 3 4 5 6 7 8 9 Year since 2000 (a) If you want to model the percentage figures with a function of the form f(t) = at + bt + c would you expect the coefficient a to be positive or negative? Why? HINT [See "Features of a Parabola" in this section.] We would expect the coefficient to be negative because the curve is concave up. We would expect the coefficient to be positive because the curve is concave down. We would expect the coefficient to be negative because the curve is concave down. We would expect the coefficient to be positive because the curve is concave up. (b) Which of the following models best approximates the data given? (Try to answer this without actually computing values.) f(t) = 0.04t2 + 0.3t – 6 f(t) = -0.04t2 + 0.3t – 6 f(t) = -0.04t2 + 0.3t + 6 f(t) = 0.04t2 + 0.3t + 6 (c) What is the nearest year that would correspond to the vertex of the graph of the correct model from part (b)? What is the danger of extrapolating the data in either direction? Extrapolating in either direction leads one to predict eventually 100 for the percentage, which isn't possible. Extrapolating in either direction leads one to predict eventually 0 for the percentage, which isn't possible. Extrapolating in either direction leads one to predict only positive values for the percentage, which isn't possible. Extrapolating in either direction leads one to predict eventually negative values for the percentage, which isn't possible. Need Help? Read It Percentage