Question

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

f(t) = 1.1t2 - 2.5t + 1.5

The average rate of change of f(t) from t = 3 to t = 5 is ______ thousand owners per year.

Answer 1

Average rate of change from a to b = (f(b) - f(a))/(b - a) = {[1.1(5)^2 - 2.5(5) + 1.5] - [1.1(3)^2 - 2.5(3) + 1.5]} / (5 - 3) = (16.5 - 3.9) / 2 = 12.6 / 2 = 6.3

Therefore, the average rate of change of f(t) from t = 3 to t = 5 is 6.3 thousand owners per year.

Answer 2

6.3

Explanation:

• The number of car owners f(t) in year 5 is found by plugging in 5 into t of the equation:

`f(5)=1.1(5)^(2)-2.5(5)+1.5=16.5`

• The number of car owners f(t) in year 3 is found by plugging in 3 into t of the equation:

`f(3)=1.1(3)^(2)-2.5(3)+1.5=3.9`

So there is a change of
`16.5-3.9=12.6` in the 2 years. So to get per year, we divide 12.6 by 2, to get:

`(12.6)/(2)=6.3`

Hence, "The average rate of change of f(t) from t = 3 to t = 5 is 6.3 thousand owners per year."