a final exam, what is the average

Question

Students took a final exam, in the equivalent form of the exam at monthly intervals, there after. The average score S(t), in per cent after t months was found to be given by   S(t)=68-20log (t+l),t>_ 0.

 

a, what is the average score when initially took the test?

 

b. what was the score after 14 months?

 

 

c. At what time was the average score 40%

Answer 1

 a) 

 

  t= 0

 

  S(t) = 68 - 20 log ( 0 +1) = 68

 

b)  S( t) = 68 - 20 log( t+1) =

                68 -20 log 15= 44.48

 

  Just need to plug in values of t into the given equation. 

Answer 2

Part a) t=0

S(0) = 68-20*log(0+1) = 68

 

Part b) t=14

S(14) = 68-20-log(14+1) = 44.48

 

Part c) S(t) = 40

40=68-20*log(t+1)

20*log(t+1)=28

log(t+1)=28/20=1.4

t+1=10^1.4=25.12

t=24.12

 

The answer is 24 since the test is only taken at monthly intervals. Plugging 24 into the function gives a score of 40.04, very close to 40.