Question

The function below shows the number of car owners f(t), in thousands, in a city in different years t:

f(t) = 0.25t2 − 0.5t + 3.5

The average rate of change of f(t) from t = 2 to t = 6 is ______ thousand owners per year.

Answer 1

1.5 thousand owners per year.

Explanation:

Number of car owners is represented by the function as

f(t) = 0.25t² - 0.5t + 3.5

Where 't' is time in years.

Now we have to find the rate of change of f(t) from t = 2 to t = 6

or
`(f(6)-f(2))/(6-2)`

f(6) = 0.25 × 36 - 0.5 × 6 + 3.5

= 9 - 3 + 3.5

= 9.5

f(2) = 0.25 × 4 - 0.5 × 2 + 3.5

= 1 - 1 + 3.5

= 3.5

Now average rate of change
`(f(6)-f(2))/(6-2)`=
`(9.5-3.5)/(6-2)`

`=(6)/(4)`

= 1.5 thousand owners per year.