exams scores

Question

. Students in a math class took a final exam and then took equivalent forms of the exam at monthly intervals thereafter. The average score f(t), as a percent, after t months was found to be given by the function f(t)=88-15ln(t+1), 0≤t≤12.

(a) What was the average score on the original exam?
(b) What was the average score after 2 months? 4 months? 6 months? 8 months? 10 months? One year?

Answer 1

a). The score for the original exam is when t =0, so f(t) = 88 - ln (1) = 88 - 0 = 88

b). Plug in t = 2, 4, etc ... One year is 12 months.

Answer 2

a)

      f(t) = 88 - 15 ln( t+1)

 

      f(0) = 88 - 15 ln1 = 88 - 15(0) = 88

 

  b) f(2) = 88 - 15 ln( 2+1) =

               88 - 15 ln(3) = 86.9

       f(4) = 88 - 15 ln (5) = 88 - 15 ( 1.61) = 63.85

 

       f(6) =

 

      f(8) =

 

       f( 10) =

     

       f(12) =