Chapter 4.1, Problem 73E

Use a calculator with on $\boxed{y^x}$ 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.

The data can he modeled by

$f\left(x\right)=x+31\text{ and }g\left(x\right)=32\cdot 7e^{0\cdot 0217x},$

in which f(x) and g(x) represent the percentage of high school seniors who applied to more than three colleges x years after 1980. Use these functions to solve Exercises 71-72. Where necessary, round answers to the nearest percent.

In college, we study large volumes of information -information that, unfortunately, we do not often retain for

very long. The function

$f\left(x\right)=80e^{-0.5x}+20$

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 fearned.

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).