Answer:
a) 88
b) F ( 2 ) = 71.5 , F ( 4 ) = 63.9 , F ( 6 ) = 58.8 , F ( 12 ) = 49.5
c) See explanation
Step-by-step explanation:
Solution:-
- 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 was modeled by a function f(t), given:
f ( t ) = 88 - 15*Ln ( t + 1 )
Interval: 0 ≤ t ≤ 12 , t : Months
- The average score obtained by the group on the original exam can be determined from the given relation at t = 0 months. Plug the value of t = 0 in the given relation to determine the average score on original exam:
f ( 0 ) = 88 - 15*Ln ( 0 + 1 )
f ( 0 ) = 88 - 15*Ln ( 1 ) = 88 - 15*0
f ( 0 ) = 88
Answer: The average score on the original exam was 88 .
- The average score obtained by the group on the exam after two months can be determined from the given relation at t = 2 months. Plug the value of t = 2 in the given relation to determine the average score on the exam:
f ( 2 ) = 88 - 15*Ln ( 2 + 1 )
f ( 2 ) = 88 - 15*Ln ( 3 ) = 88 - 16.47918
f ( 2 ) = 71.520
Answer: The average score on the exam after two months was 71.5
- The average score obtained by the group on the exam after four months can be determined from the given relation at t = 4 months. Plug the value of t = 4 in the given relation to determine the average score on the exam:
f ( 4 ) = 88 - 15*Ln ( 4 + 1 )
f ( 4 ) = 88 - 15*Ln ( 5 ) = 88 - 24.14156
f ( 4 ) = 63.858
Answer: The average score on the exam after four months was 63.9
- The average score obtained by the group on the exam after six months can be determined from the given relation at t = 6 months. Plug the value of t = 6 in the given relation to determine the average score on the exam:
f ( 6 ) = 88 - 15*Ln ( 6 + 1 )
f ( 6 ) = 88 - 15*Ln ( 7 ) = 88 - 29.18865
f ( 6 ) = 58.811
Answer: The average score on the exam after six months was 58.8
- The average score obtained by the group on the exam after a year can be determined from the given relation at t = 12 months. Plug the value of t = 12 in the given relation to determine the average score on the exam:
f ( 12 ) = 88 - 15*Ln ( 12 + 1 )
f ( 12 ) = 88 - 15*Ln ( 13 ) = 88 - 38.47424
f ( 12 ) = 49.525
Answer: The average score on the exam after a year was 49.5
- The function F ( t ) i.e the average score of the group for the equivalent exams they took over the course of months is shown by a decreasing curve.
- The average score decreases as time passes by. This hints towards the material retention of the students decreases with time because they score less after every successive exam.
