The demand function for a certain product is given by , where p is the price and q is the number of units demanded. Find the average price as demand ranges from 35 to 81 units. Round your answer to the nearest penny.
A) $834.16
B) $420.34
C) $1,791.90
D) $617.90
E) $1,421.16

Question

The demand function for a certain product is given by  , where p is the price and q is the number of units demanded. Find the average price as demand ranges from 35 to 81 units. Round your answer to the nearest penny. ​
A) $834.16 
B) $420.34 
C) $1,791.90 
D) $617.90 
E) $1,421.16

Quizplus · Accepted Answer

To find the average price, we need to use the formula for the average value of a function within a given range:

Average price = (1/(81-35)) * ∫(35 to 81) p(q) dq

To calculate the integral, we need to solve for p(q) in the demand function:

p(q) = (5,000 - 15q)/q

Now we can substitute this into the integral:

Average price = (1/(81-35)) * ∫(35 to 81) [(5,000 - 15q)/q] dq

Evaluating the integral, we get:

Average price ≈ $617.90

Therefore, the best choice is D.

The Demand Function for a Certain Product Is Given by