The monthly demand for a certain brand of perfume is given by the demand equation p = 100e^-0.0002x + 125 where p denotes the retail unit price (in dollars) and x denotes the quantity (in 1-oz bottles) demanded. (a) Find the rate of change of the price per bottle when x = 1000 and when x = 2000. (Round your answers to four decimal places.) x = 1000 dollars/bottle x = 2000 dollars/bottle (b) What is the price per bottle when x = 1000? When x = 2000? (Round your answers to the nearest cent.) x = 1000 $ x = 2000 $
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So, we first need to find the derivative of P with respect to x. The derivative of P with respect to x is given by dP/dx = 100 * 0.0002 * e^0.0002x. Now, we can substitute x = 1000 and x = 2000 into this derivative to find the rate of change at these Show more…
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