Students in a psychology class took a final examination As p

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) = 88 - 15 ln(t + 1), 0 lessthanorequalto t lessthanorequalto 12. What was the average score on the original exam? What was the average score after 2 months? 4 months? 6 months? 8 months? 10 months? one year? 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.

Solution

f(t)=88 - 15 ln(t+ 1)

a. To find the average score in the original exam,we have to plug t=0

f(0)=88-15 ln(0+1)

f(0)= 88-15(0)=88

b. Average score after 2 months

f(2)= 88-15ln(2+1)= 71.52

Average score after 4 months

f(4)=88-15ln(4+1)= 63.86

Average score after 6 months

f(6)= 88-15 ln(6+1)=58.81

Average score after 8 months

f(8)=88 - 15 ln(8+1)= 55.04

After 10 months

f(10)=88-15 ln(10+1)=52.03

After 1 year

f(12)= 88-15ln(12+1)=49.53