Question

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

f(t) = 1.1t^2 − 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

The Average Rate of  Change is the change of the function's value to the change in the variable t along some close interval

$f(t) = 1.1~t^2 - 2.5t + 1.5\\~\\f(5)=1.1~(5)^2 - 2.5(5) + 1.5=16.5\\~\\~\\f(3)=1.1~(3)^2 - 2.5(3) + 1.5=3.9\\~\\~\\ARC= \frac{f(5)-f(3)}{5-3} = \frac{16.5-3.9}{5-3} =6.3$

I hope that helps!