Question

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 $

Name: the monthly demand for a certain brand of perfume is given by the demand equation p 100e00001x 75 where p denotes the retail unit price in dollarsbottle and x denotes the quantity in 1 oz bo 93796
Uploaded: 2022-11-30T11:30:31-08:00
Duration: 5 min 19 s
Channel: Adi S
Description: the monthly demand for a certain brand of perfume is given by the demand equation p 100e00001x 75 where p denotes the retail unit price in dollarsbottle and x denotes the quantity in 1 oz bo 93796

          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      $

Added by Connie Y.

Calculus: Early Transcendentals

James Stewart 8th Edition

Instant Answer

Solved by Expert Adi S

11/30/2022

Step 1

The demand equation is given by $ p = 100e^{-0.0001x} + 75 $. To find the rate of change of the price per bottle with respect to the quantity demanded, we need to differentiate this equation with respect to x. Using the chain rule, the derivative of $ p $ with Show more…

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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 $