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.)

Question

Ciara Ingram

Mathematics

28 January, 01:27

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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Answers (1)

Know the Answer?

Ryder Chang · Answer 1

(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