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15 June, 01:29

In 2007, there were more than 8.14 million cars for sale. Over the next 3 years, the number of cars decreased by 23%. Write an exponential growth or decay model given by the number of c cars over t years after 2007. Use this model to estimate how many cars there will be in 2013?

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  1. 15 June, 01:53
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    c = 8.14 million * (0.9166) ^t

    4.83 million

    Step-by-step explanation:

    dа ta:

    t = y - 2007

    c₀ = 8.14 million

    c₃ = 23 % less than c₁

    Part 1. Calculate c₃

    c₃ = c₀ (1 - 0.23) = 0.77c₀

    Part 2. Calculate r

    c₃ = c₀r^t

    0.77c₀ = c₀r³

    0.77 = r³ Divided each side by c₀

    r = 0.9166 Took the cube root of each side

    The explicit decay model is c = 8.14 million * (0.9166) ^t

    Part 3. Prediction

    t = 2013 - 2007 = 6

    c = c₀r^t = 8.14 million * (0.9166) ⁶ = 8.14 million * 0.5929 = 4.83 million

    The model predicts that there will be 4.83 million cars for sale in 2013.
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