Use a calculator with an e^x key to solve Exercises 71–76. The bar graph shows the percentage of U.S. high school seniors who applied to more than three colleges for selected years from 1980 through 2013.In college, we study large volumes of information— information that, unfortunately, we do not often retain for very long. The function f(x) = 80e^-0.5x + 20 describes the percentage of information, f(x), that a particular person remembers x weeks after learning the information.

a. Substitute 0 for x and, without using a calculator, find the percentage of information remembered at the moment it is first learned.

b. Substitute 1 for x and find the percentage of information that is remembered after 1 week.

c. Find the percentage of information that is remembered after 4 weeks.

d. Find the percentage of information that is remembered after one year (52 weeks).

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Percentage of High School Seniors 80% 70% 60% 50% 40% 30% 20% 10% 32 Percentage of U.S. High School Seniors Applying to More Than Three Colleges 43 44 51 55 61 69 ********** 1980 1990 1995 2000 2005 2010 2013 Year