Question

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.)

Answer 1

15 units per dollar

Step-by-step explanation:

Given that,

`N(p)=100 - 3p^(2)`

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.