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 ≤ t ≤ 12.

a. what was the average score on the original exam?
the average score on the original exam was 75. (type a whole number.)

b. what was the average score after 6 months?
the average score after 6 months was
(round to the nearest tenth as needed.)

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.

Explanation:

Step1: Identify the function and t value

The function is \( f(t) = 75 - 15\ln(t + 1) \), and we need to find the average score after 6 months, so \( t = 6 \).

Step2: Substitute t into the function

Substitute \( t = 6 \) into \( f(t) \): \( f(6)=75 - 15\ln(6 + 1)=75 - 15\ln(7) \).

Step3: Calculate the natural logarithm

First, calculate \( \ln(7)\approx1.9459 \).

Step4: Multiply and subtract

Then, \( 15\times1.9459\approx29.1885 \). Now, \( f(6)=75 - 29.1885\approx45.8115 \).

Step5: Round to the nearest tenth

Rounding \( 45.8115 \) to the nearest tenth gives \( 45.8 \).

Answer:

45.8