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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

Verified Answer :

meerkat18

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.

Answer:

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

Step-by-step 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

\(m=\frac{f(x_2)-f(x_1)}{x_2-x_1}\)

\(m=\frac{f(8)-f(5)}{8-5}\)

\(m=\frac{6.5-1.25}{3}\)

\(m=1.75\)

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

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