Question

HELP PLEASE!

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

f(t) = 0.25t2 - 0.5t + 3.5

The average rate of change of f(t) from t = 2 to t = 6 is_________ thousand owners per year. (3 points)

Answer 1

@Michele_Laino @nincompoop

Answer 2

the average rate R, is given by the subsequent formula:
\[R = \frac{{f\left( 6 \right) - f\left( 2 \right)}}{{6 - 2}}\]

Answer 3

so it would be R= f(4) over 4?? @Michele_Laino

Answer 4

Rate of change is the change in y over the change in x. So plug in t = 2 into the equation to find f(2) and t = 6 into the equation to find f(6). Then do [ f(x) - f(2) ] / (6-2)

Answer 5

f(6) - f(2)

My bad

Answer 6

so then would the answer be 4?

Answer 7

cause it would be f(4) over 4?

Answer 8

f(2) = 3.5
f(6) = 9.5


9.5 - 3.5 = 6
6 -2 = 4

Rate of change is 6/4 = 3/2

Answer 9

no, you have to compute this quantity:
\[\begin{gathered}
R = \frac{{f\left( 6 \right) - f\left( 2 \right)}}{{6 - 2}} = \hfill \\
\hfill \\
= \frac{{\left( {0.25 \times 36 - 0.5 \times 6 + 3.5} \right) - \left( {0.25 \times 4 - 0.5 \times 2 + 3.5} \right)}}{4} = ...? \hfill \\
\end{gathered} \]

Answer 10

so 1.5 would be the rate of change

Answer 11

Yes

Answer 12

ok thank you soo much! :)