Question

the function ( f(x)=90e^{-0.4x}+10 ) describes the percentage of information, ( f(x) ), that a particular person remembers ( x ) weeks after learning the info
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).
a. at the moment it is first learned, 100 % of the information is remembered.
(round to one decimal place as needed.)
b. after one week, ( square % ) of the information is remembered.
(round to one decimal place as needed.)

Explanation:

Step1: Substitute \(x = 1\) into the function \(f(x)=90e^{-0.4x}+10\)

$$
LATEXBLOCK0
$$

Step2: Recall that \(e^{-a}=\frac{1}{e^{a}}\), so \(e^{-0.4}=\frac{1}{e^{0.4}}\approx\frac{1}{1.4918}\approx0.6703\)

$$
LATEXBLOCK1
$$

Answer:

\(70.3\)