Question

students in a psychology class took a final examination. as part of an experiment to see how much of the course content they remembered over time, they took equivalent forms of the exam in monthly intervals thereafter. the average score for the group ( f(t) ), after ( t ) months was modeled by the function ( f(t) = 75 - 15 ln(t + 1) ), ( 0 leq t leq 12 ).

a. what was the average score on the original exam?

b. what was the average score after 6 months?

c. sketch the graph of ( f ) (either by hand or with a graphing utility.) describe what the graph indicates in terms of the material retained by the students.

a. the average score on the original exam was (\boxed{quad}).
( type a whole number. )

Explanation:

Step1: Identify t for original exam

The original exam is at \( t = 0 \) (since \( t \) is the number of months after the original exam).

Step2: Substitute t = 0 into f(t)

The function is \( f(t)=75 - 15\ln(t + 1) \). Substitute \( t = 0 \):
\( f(0)=75 - 15\ln(0 + 1) \)
Since \( \ln(1)=0 \), this simplifies to \( f(0)=75 - 15\times0 = 75 \).

Answer:

75