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 + 1.5The average rate of change of f(t) from t = 3 to t = 5 is ______ thousand owners per year.Answer for Blank 1:

Answer 1

The average rate of change is :
`6.3`

Explanation:

The number of car owners is modeled by the function;

`f(t)=1.1t^2-2.5t+1.5`, where t is the different number of years.

The average rate of change of f(t) from t=3 to t=5 is simply the slope of the secant line connecting:

(3, f(3)) and (5,f(5))

Which is given by:

`(f(5)-f(3))/(5-3)`

Now, we substitute t=3 into the function to get;

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

`f(3)=3.9`

We substitute t=5 into the function to get;

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

`f(5)=16.5`

Therefore the average rate of change is :
`(14.5-3.9)/(2)=6.3`