The price p (in dollars) and demand x for wireless headphones are related by x = 7,000- 0.15 p^2. The current price of $110 is decreasing at a rate $5 per week. Find the associated revenue function R(p) and the rate of change (in dollars per week) of revenue.

Total Revenue Function = 7000p - 0.15 p^3

Rate of change per unit price change = 7000 - 0.45 p^2

Step-by-step explanation:

x = 7000 - 0.15 p^2  [Quantity given]

Total Revenue is the total value of receipts from sale. TR = Price X Quantity

TR Function = p.x

= p (7000 - 0.15 p^2)  = 7000p - 0.15 p^3  

Rate of change in revenue, due to change in price

dTR / dP = 7000 - 0.45 p^2

iu

step-by-step explanation: