Question

students in a fifth - grade class were given an exam. during the next 2 years, the same students were retested several times. the average score was given by the model:
$f(t)=83 - 3\log(t + 1),\\ 0\leq t\leq24$
where $t$ is the time in months. round all answers to nearest tenth.
a) what is the average score on the original exam?
b) what was the average score after 6 months?
c) what was the average score after 18 months?

Explanation:

Step1: Find the average score on the original exam (t = 0)

Substitute \(t = 0\) into the function \(f(t)=83 - 3\log(t + 1)\).

$$
LATEXBLOCK0
$$

Since \(\log(1)=0\), then \(f(0)=83-3\times0 = 83.0\)

Step2: Find the average score after 6 months (t = 6)

Substitute \(t = 6\) into the function \(f(t)=83 - 3\log(t + 1)\).

$$
LATEXBLOCK1
$$

Step3: Find the average score after 18 months (t = 18)

Substitute \(t = 18\) into the function \(f(t)=83 - 3\log(t + 1)\).

$$
LATEXBLOCK2
$$

Answer:

a) \(83.0\)
b) \(80.5\)
c) \(79.2\)