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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)=100 - 3 p^2​; 1 < p < 4 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 nothing boxes per dollar. ​(Type an integer or a​ decimal.)

Respuesta :

Answer:

15 units per dollar

Explanation:

Given that,

[tex]N(p)=100 - 3p^{2}[/tex]

change in price from ​$2 to ​$3

= $3 - $2

= $1

N(3)=100 - 3(3)^{2}

     = 100 - 27

     = 73

N(2)=100 - 3(2)^{2}

     = 100 - 12

     = 88

Therefore, the average rate of change of demand for a change in price from ​$2 to ​$3 is as follows:

= [N(3) - N(2)] ÷ Change in price

= [73 - 88] ÷ 1

= - 15

Hence, the average rate of change of demand decreases at the rate of 15 units per dollar for a change in price from ​$2 to ​$3.

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