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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.

Respuesta :

Answer:

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

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