Students in a college algebra class were given a final exam in May and subsequently retested montly with an equivalant exam. The average score (overline{x}) for the class is given by the human memory model overline{x} = 86-15log(t+1) where t is the time in months after the final exam. What is the average score 5 months after the final exam? Give your answer correct to the nearest hundreth.

Question
Upper level algebra
Students in a college algebra class were given a final exam in May and subsequently retested montly with an equivalant exam. The average score $$(\overline{x})$$ for the class is given by the human memory model $$\overline{x} = 86-15\log(t+1)$$
where t is the time in months after the final exam. What is the average score 5 months after the final exam? Give your answer correct to the nearest hundreth.

2021-01-01
Step 1
We are given that students we re-tested on College Algebra, on a monthly basis, after final exam, starting in May.
The average score $$(\overline{x})$$ for the class is given by the human memory model, $$\overline{x} = 86 - 15\log(t+1)$$,
where t is the time in months after the final exam.
We are asked to find the average score 5 months after the final exam.
Step 2
Noe, to find the average score 5 months after the final exam, we substitute t=5 in the formula
$$\overline{x} = 86 - 15\log(t+1)$$.
This gives us
$$\overline{x} = 86 - 15\log(5+1)$$,
$$\Rightarrow \overline{x} = 86 -11.672$$
$$\Rightarrow \overline{x} = 74.328$$

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