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.

Numerical Answers Expected!

Answer for Blank 1:

Answer 1

f(t) = 1.1t² - 2.5t + 1.5

t = 3
f(3) = 1.1(3²) - 2.5(3) + 1.5
f(3) = 1.1(9) - 7.5 + 1.5
f(3) = 9.9 - 7.5 + 1.5
f(3) = 11.4 - 7.5
f(3) = 3.9

t = 5
f(5) = 1.1(5²) - 2.5(5) + 1.5
f(5) = 1.1(25) - 12.5 + 1.5
f(5) = 27.5 - 12.5 + 1.5
f(5) = 29 - 12.5
f(5) = 16.5

3.9 + 16.5 = 20.4
20.4 / 2 = 10.2
10.2 x 1,000 = 10,200 owners per year.