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)=83 - 12 ln(t + 1), 0≤t≤12. a. what was the average score on the original exam? b. what was the average score after 8 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 (type a whole number.)

Explanation:

Step1: Substitute t = 0 for original exam

When t = 0, we use the function f(t)=83 - 12ln(t + 1). Substitute t = 0 into the function: f(0)=83-12ln(0 + 1).
Since ln(1)=0, then f(0)=83-12×0.

Step2: Calculate f(0)

f(0)=83 - 0=83.

Step3: Substitute t = 8 for 8 - months

When t = 8, f(8)=83-12ln(8 + 1).
We know that ln(9)≈2.1972. Then f(8)=83-12×2.1972.
f(8)=83 - 26.3664 = 56.6336≈57.

Step4: Analyze graph for part c

The function f(t)=83 - 12ln(t + 1) is a decreasing - function. As t increases from 0 to 12, the value of f(t) decreases. This indicates that the average score of the students (and thus the amount of course material they retain) decreases over time. The graph starts at (0, 83) and gradually slopes downwards as t moves from 0 to 12.

Answer:

a. 83
b. 57
c. The graph of y = f(t) is a decreasing curve starting at (0, 83) and decreasing as t increases from 0 to 12, indicating that the amount of course - material retained by students decreases over time.