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5 August, 21:17

Suppose customers in a hardware store are willing to buy N (p) boxes of nails at p dollars per box, as given by the following function. N (p) = 80-5p2; Find the average rate of change of demand for a change in price from $2 to $3. The average rate of change of demand for a change in price from $2 to $3 is - 25 boxes per dollar. (Type an integer or a decimal.) Find the instantaneous rate of change of demand when the price is $2. The instantaneous rate of change of demand when the price is $2 is - 20 boxes per dollar. (Type an integer or a decimal.) Find the instantaneous rate of change of demand when the price is $3. The instantaneous rate of change of demand when the price is $3 is boxes per dollar. (Type an integer or a decimal.)

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  1. 6 August, 00:43
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    (a) - 25 boxes per dollar

    (b) - 20 boxes per dollar

    Step-by-step explanation:

    Given that,

    Consumer's willing to buy boxes of nails at p dollars per box:

    N (p) = 80 - 5p^{2}

    (a) Change in price from $2 to $3.

    N (2) = 80 - 5 (2) ^{2}

    = 80 - 20

    = 60

    N (3) = 80 - 5 (3) ^{2}

    = 80 - 45

    = 35

    Therefore, the average rate of change of demand is

    = [N (3) - N (2) ] : (3 - 2)

    = 35 - 60

    = - 25 boxes per dollar.

    (b) N (p) = 80 - 5p^{2}

    Now, differentiating the above function with respect to p,

    N' (p) = - 10p

    Therefore, the instantaneous rate of change of demand when the price is $2 is calculated as follows:

    N' (p) = - 10p

    N' (2) = - 10 * 2

    = - 20 boxes per dollar
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