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26 April, 20:56

For which function is the average rate of change over the interval 1 < x < 5 greater than the average rate of change over the same interval for the function g (x) = 1.8x2?

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  1. 26 April, 21:20
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    The average rate of change of g (x) = 1.8x² with interval 1 < x < 5 is 10.8

    Step-by-step explanation:

    Given

    g (x) = 1.8x²

    Interval 1 < x < 5

    The average rate of change of the function g (x) on the interval [a, b] is calculated using the following formula:

    Average Rate of change = (g (b) - g (a)) / (b - a)

    Where a and b are values from the interval.

    a = lower Interval = 1

    b = upper Interval = 5

    First, we need to calculate g (b) and g (a)

    Given that g (x) = 1.8x²

    g (a) = g (5) = 1.8 * 1²

    g (a) = 1.8 * 1

    g (a) = 1.8

    Then we calculate g (a)

    g (b) = g (5) = 1.8 * 5²

    g (b) = 1.8 * 25

    g (b) = 45

    We then calculated the average Rate of change by substituting values in = (g (b) - g (a)) / (b - a)

    Average Rate of Change = (45 - 1.8) / (5 - 1)

    Average Rate of Change = 43.2/4

    Average Rate of Change = 10.8

    Hence, the average rate of change of g (x) = 1.8x² with interval 1 < x < 5 is 10.8
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