Question

(09.01) 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

The average rate of change is:

r=(f(b)-f(a))/(b-a), where a and b are the beginning and end of the interval.

So in this case:

r=(.25(6^2)-.5(6)+3.5-.25(2^2)+.5(2)-3.5)/(6-2)

r=1.5

So the average rate of change of car owners is 1.5 thousand owners per year.

Answer 2

Answer: The average rate of change of f(t) from t = 2 to t = 6 is 1.5 thousand owners per year.

Explanation:

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

`f(t) = 0.25^2 - 0.5t + 3.5`

Now,

`f(2) = 0.25(2)^2 - 0.5(2) + 3.5=3.5\\\\= f(6) = 0.25(6)^2-0.5(6)+ =9.5`

Now, the average rate of change of f(t) from t = 2 to t = 6 is given by :-

`k=(f(6)-f(2))/(6-2)\\\\=(9.5-3.5)/(4)=1.5`

Hence, the average rate of change of f(t) from t = 2 to t = 6 is 1.5 thousand owners per year.