The monthly demand for a certain brand of perfume is given by the demand equation p = 100e−0.0001x + 75 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 = 1,000 and when x = 4,000. (Round your answers to four decimal places.) x = 1,000         dollars/bottle  x = 4,000                 dollars/bottle (b) What is the price per bottle (in dollars) when x = 1,000? When x = 4,000? (Round your answers to the nearest cent.) x = 1,000      $  x = 4,000      $

Algebra and Trigonometry (MindTap Course List)
4th Edition
ISBN:9781305071742
Author:James Stewart, Lothar Redlin, Saleem Watson
Publisher:James Stewart, Lothar Redlin, Saleem Watson
Chapter2: Functions
Section2.4: Average Rate Of Change Of A Function
Problem 4.2E: bThe average rate of change of the linear function f(x)=3x+5 between any two points is ________.
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The monthly demand for a certain brand of perfume is given by the demand equation
p = 100e−0.0001x + 75
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 = 1,000 and when x = 4,000. (Round your answers to four decimal places.)
x = 1,000         dollars/bottle  x = 4,000                 dollars/bottle
(b)
What is the price per bottle (in dollars) when x = 1,000? When x = 4,000? (Round your answers to the nearest cent.)
x = 1,000      $  x = 4,000      $ 
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