Question

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

f(t) = 0.25t2 - 1.5t + 2.5

The average rate of change of f(t) from t = 5 to t = 8 is ______ thousand per year

Answer 1

The average rate of change of f(t) from t = 5 to t = 8 is 1.75 thousand per year.

Explanation:

The given function is

`f(t)=0.25t^2-1.5t+2.5`

We have to find the average rate of change of f(t) from t = 5 to t = 8.

Substitute t=5

`f(5)=0.25(5)^2-1.5(5)+2.5=1.25`

Substitute t=8

`f(8)=0.25(8)^2-1.5(8)+2.5=6.5`

The average rate of change is defend as

`m=(f(x_2)-f(x_1))/(x_2-x_1)`

`m=(f(8)-f(5))/(8-5)`

`m=(6.5-1.25)/(3)`

`m=1.75`

Therefore the average rate of change of f(t) from t = 5 to t = 8 is 1.75 thousand per year.

Answer 2

we are given the function f(t) = 0.25t2 - 1.5t + 2.5 and is asked in the problem to determine the average rate of change from t equal to 5 and t equal to 8. In this case, we substitute t with 5 and 8 first that is equal to 1.25 and 6.5, respectively. The rate of change is (6.5-1.25)/(8-5) equal to 1.75 thousand per year.