Texts: Price of Perfume
The monthly demand for a certain brand of perfume is given by the demand equation:
p = 100e^(-0.0002x) + 100
where p denotes the retail unit price (in dollars/bottle) and x denotes the quantity (in 1-oz bottles) demanded.
(a)
Find the rate of change of the price per bottle (in dollars) when x = 2,000 and when x = 3,000. (Round your answers to four decimal places.)
x = 2,000 dollars/bottle
x = 3,000 dollars/bottle
(b)
What is the price per bottle (in dollars) when x = 2,000? When x = 3,000? (Round your answers to the nearest cent.)
x = $2,000
x = $3,000