For selected years from 1985 and projected to 2035, the following table shows the U.S. energy use per dollar of GDP, viewed as a percent of the 1980 usage. Thus, in 2000, U.S. energy use per dollar of GDP was 67% of what it was in 1980. Suppose the rate of change of energy use per dollar of GDP can be modeled by

dE/dt = 0.00468(0.4t + 2)² - 0.104(0.4t + 2) - 0.56

percentage points per year, where t is the number of years past 1980.

(a) Use integration and the data point for 1990 to find the function E(t) that models the energy use per dollar of GDP. Use 2 significant digits.

(b) Graph the model from part (a) with the data in the table.

(c) Find the model’s predicted energy use per dollar of GDP in 2025.

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Energy Use per Dollar of GDP Year Percent Year Percent 1985 83 2015 51 1990 79 2020 45 1995 75 2025 41 2000 67 2030 37 2005 60 2035 34 2010 56