Question

The number x of stereo speakers a retail chain is willing to sell per week at a price of p dollars is given by x = 83 √p + 23 – 400. Find the supply and instantaneous rate of change of supply when the price is 75 dollars. Supply = Instantaneous rate of change of supply =

Answer 1

The supply and the instantaneous rate of change of supply at a price of 75 dollars are found by substituting the price into the given formula and taking its derivative, respectively.

Step-by-step explanation:

The number of stereo speakers x that a retail chain is willing to sell per week at a price of p dollars is given by x = 83 √p + 23 – 400. To find the supply when the price is 75 dollars, we substitute p with 75 in the equation:

x = 83 √75 + 23 – 400

Now, to find the instantaneous rate of change of supply, we take the derivative of x with respect to p, which represents the rate at which the supply changes with a change in price:

dx/dp = 83/(2√p)

When the price is 75 dollars, the instantaneous rate of change is:

dx/dp = 83/(2√75)

After calculating these values, we can provide the exact supply and the instantaneous rate of change of the supply at the price of $75.