students in a biology class just took a final exam. a formula for predicting the average exam grade on a similar test t months later is.
s(t)=78-15log(t+1)
(a)find the students average score when they first took the final exam.
(b)what would be the expected average score be on a retest after 4 months.
I know the answers I just am not sure how to work the problem to get them.
(a)78
(b)67.5
Please help me with the working of these problems.
Thank you
To find the average score when the students first took the final exam, we need to substitute t = 0 into the formula for s(t).
(a) Substitute t = 0 into the formula s(t)=78-15log(t+1):
s(0) = 78 - 15log(0 + 1)
s(0) = 78 - 15log(1)
Since log(1) = 0, s(0) = 78 - 15(0)
Therefore, the average score when the students first took the final exam is 78.
To find the expected average score on a retest after 4 months, we need to substitute t = 4 into the formula for s(t).
(b) Substitute t = 4 into the formula s(t)=78-15log(t+1):
s(4) = 78 - 15log(4 + 1)
s(4) = 78 - 15log(5)
Now, we need to calculate the value of log(5), which is approximately 0.6990 (rounded to four decimal places).
Let's substitute that value back into the equation:
s(4) ≈ 78 - 15(0.6990)
s(4) ≈ 78 - 10.485
Therefore, the expected average score on a retest after 4 months is approximately 67.515 (rounded to three decimal places).