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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)

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  1. anonymous
    • one year ago
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    @Michele_Laino @nincompoop

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

  3. anonymous
    • one year ago
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    so it would be R= f(4) over 4?? @Michele_Laino

  4. anonymous
    • one year ago
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    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
    • one year ago
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    f(6) - f(2) My bad

  6. anonymous
    • one year ago
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    so then would the answer be 4?

  7. anonymous
    • one year ago
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    cause it would be f(4) over 4?

  8. anonymous
    • one year ago
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    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
    • one year ago
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    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
    • one year ago
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    so 1.5 would be the rate of change

  11. anonymous
    • one year ago
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    Yes

  12. anonymous
    • one year ago
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    ok thank you soo much! :)

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