Yasmin

2020-12-31

Students in a college algebra class were given a final exam in May and subsequently retested montly with an equivalant exam. The average score $\left(\stackrel{―}{x}\right)$ for the class is given by the human memory model $\stackrel{―}{x}=86-15\mathrm{log}\left(t+1\right)$
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.

falhiblesw

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 $\left(\stackrel{―}{x}\right)$ for the class is given by the human memory model, $\stackrel{―}{x}=86-15\mathrm{log}\left(t+1\right)$,
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
$\stackrel{―}{x}=86-15\mathrm{log}\left(t+1\right)$.
This gives us
$\stackrel{―}{x}=86-15\mathrm{log}\left(5+1\right)$,
$⇒\stackrel{―}{x}=86-11.672$
$⇒\stackrel{―}{x}=74.328$

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