13. (Total-3 Points) Students participating in a psychology experiment attended

Question

13. (Total-3 Points) Students participating in a psychology experiment attended several lectures and were given an exam. Every month for the next year, the students were retested to see how much of the material they remembered. The average scores for the group are given by the function f( 90-15 logt +1),OsI3 12, where t is the time in months). Algebraically answer the following: a. (1 Point) What was the average score on the original exam (t 0)? b ( Point) What was the average score after 12 months? c. (1 Point) When will the average score decrease to 75?

Explanation / Answer

f(t) = 90 - 15 log ( t +1 )

a) average score in original exam

plugging t = 0

f(t) = 90 - 15 log ( 1)

so avearge score in original test is 90

b) average score after 12 months

plug t = 12

f(t) = 90 - 15 log ( 12+1 )

= 73.29

avearge score after 12 months = 73.29

c) plugging f(t) = 75

75 = 90 - 15 log ( t +1 )

75 - 90 = -15 log ( t+1 )

1 = log (t+1)

10^1 = t +1

t = 9

so , score decreases to 75 after 9 months

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