4. Educational psychologists study memory, and have found a mathematical model that describes students' retention of material learned. Students take a test, and after some time
(t) without reviewing they take an equivalent test. The function a(t) describes students'
retention, a(t) = 78 – 12 log(t + 1) where a is the average score at time t where t is the
time in months since they first took the test.
a. What was the average score when students first took the test (t = 0)?
b. What is the average score after 6 months?
C. After how many months is the average score 60?