This is really confusing and nneds to be shown with how it was worked out.

Question

I have what I think is right; but want to know if my calculations agree.

Students in an English class took a final exam. They took equivalent forms of the exam at monthly inervals thereafter. The average score S(t ), percent, after t months was found to be given by S(t )=68 -20 log (t + 1), t ≥ 0

a. What was the average score when they initially took the test, t = 0? (show work so I can see if same answer)

b. What was the average score after 14 months? (show work to see if I'm still on the right track)

c. After what time t was the average score 40%? (show work to see if we agree)  Thank you!

Answer 1

Since the average score is the function of time, plugging time, you can get the answer.

a) S(0) = 68 -20 log (0+ 1) = 68, since log 1 = 0

b) S(14) = 68 -20 log (14 + 1) = 44.5

c) S(t) = 68 -20 log (t+ 1) = 40

Solve for t,

log(t + 1) = 28/20

t = 10^(28/20) - 1 = 24.12 months <==Answer