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 ) = 92 − 4 log 10 ⁡ ( t + 1 ) , 0 ≤ t ≤ 24 where t is the time in months.

Answer 1

Using the logarithmic function, it is found that:

a) The initial score is of 92.

b) After 6 months, the score is of 88.6.

c) After 18 months, the score is of 86.9.

The average score after t months is modeled by:

$f(t) = 92 - 4\log{(t + 1)}$

Item a:

The initial score is of f(0), hence:

$f(0) = 92 - 4\log{1} = 92 - 0 = 92$

The initial score is of 92.

Item b:

After 6 months, the score is of f(6), hence:

$f(6) = 92 - 4\log{7} = 88.6$

After 6 months, the score is of 88.6.

Item c:

After 18 months, the score is of f(18), hence:

$f(6) = 92 - 4\log{19} = 86.9$

After 18 months, the score is of 86.9.

A similar problem is given at https://brainly.com/question/24286043