## anonymous one year ago 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)

1. anonymous

@Michele_Laino @nincompoop

2. Michele_Laino

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

3. anonymous

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

4. anonymous

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)

5. anonymous

6. anonymous

so then would the answer be 4?

7. anonymous

cause it would be f(4) over 4?

8. anonymous

f(2) = 3.5 f(6) = 9.5 9.5 - 3.5 = 6 6 -2 = 4 Rate of change is 6/4 = 3/2

9. Michele_Laino

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

10. anonymous

so 1.5 would be the rate of change

11. anonymous

Yes

12. anonymous

ok thank you soo much! :)