Suppose that the demand for a product depends on the price p according to , , where p is in dollars. Find and explain the meaning of the instantaneous rate of change of demand with respect to price when .
A)-0.32. If price increases by $1, the demand will decrease approximately 0.32 units.
B)0.32. If price increases by $1, the demand will increase approximately 0.32 units.
C)-0.64. If price increases by $1, the demand will decrease approximately 0.64 units.
D)-49.84. If price increases by $1, the demand will increase approximately 49.84 units.
E)0.64. If price increases by $1, the demand will decrease approximately 0.64 units.

Question

Suppose that the demand for a product depends on the price p according to  ,  , where p is in dollars. Find and explain the meaning of the instantaneous rate of change of demand with respect to price when  . ​
A)-0.32. If price increases by $1, the demand will decrease approximately 0.32 units. 
B)0.32. If price increases by $1, the demand will increase approximately 0.32 units. 
C)-0.64. If price increases by $1, the demand will decrease approximately 0.64 units. 
D)-49.84. If price increases by $1, the demand will increase approximately 49.84 units. 
E)0.64. If price increases by $1, the demand will decrease approximately 0.64 units.

Quizplus · Accepted Answer

We can find the derivative of the demand function with respect to price by differentiating the function. Using the power rule of differentiation, we get:

dD/dp = -0.64p^(-1.64)

When p = 25, we have:

dD/dp = -0.64(25)^(-1.64) ≈ -0.032

This means that for every increase of $1 in price, the demand will decrease by approximately 0.64(1.64)/25 ≈ 0.032 units, which is equivalent to a change in demand of approximately -0.32 units. Therefore, the correct choice is C.

Suppose That the Demand for a Product Depends on the Price