Question

the function ( f(x)=60e^{-0.4x}+40 ) 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).
a. at the moment it is first learned, (square%) of the information is remembered.
(round to one decimal place as needed.)

Explanation:

Step1: Substitute \(x = 0\) into the function

We know that \(e^{0}=1\). Substitute \(x = 0\) into \(f(x)=60e^{-0.4x}+40\).

$$
LATEXBLOCK0
$$

Step2: Calculate the value

Since \(e^{0} = 1\), then \(f(0)=60\times1 + 40=100\)

Answer:

\(100.0\)