Chapter 4.4, Problem 86E

### Calculus: An Applied Approach (Min...

10th Edition
Ron Larson
ISBN: 9781305860919

Chapter
Section

### Calculus: An Applied Approach (Min...

10th Edition
Ron Larson
ISBN: 9781305860919
Textbook Problem
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# Demand The demand function for a product is given by p = 12 , 000 ( 1 − 3 3 + e − 0.001 x ) where p is the price per unit (in dollars) and x is the number of units sold. Find the number of units sold when (a) p = $500 and (b) p =$1600. Use a graphing utility to verify your results in parts (a) and (b).

(a)

To determine

To calculate: The number of units sold if the price of the product is $500, that is p=$500 when the demand function for a product is given by:

p=12,000(133+e0.001x)

Where, p is the price of the product in dollars and x is the number of units sold. Also verify the result using technology.

Explanation

Given Information:

The demand function for a product is given by:

p=12,000(133+e0.001x)

Where, p is the price of the product in dollars and x is the number of units sold.

Formula used:

The inverse property of logarithms for the expression lnex is lnex=x.

The property of logarithms for the expression ln(xy) is ln(xy)=lnxlny where x and y are real numbers greater than 0.

Calculation:

Consider the demand function, p=12,000(133+e0.001x)

Calculate the number of units sold if the price of the product is $500 by substituting p=500 in the demand function as, 500=12,000(133+e0.001x) Divide the both sides by 12,000 as, 50012,000=12,000(133+e0.001x)12,000133+e0.001x=124 Subtract 1 from both sides as, 133+e0.001x1=124133+e0.001x=1242433+e0.001x=2324 Cancel the minus sign from the both sides and simplify as, 33+e0.001x=2324 Multiply both sides by 24(3+e0.001x) as, 33+e0 (b) To determine To calculate: The number of units sold if the price of the product is$1600, that is p=\$1600 when the demand function for a product is given by:

p=12,000(133+e0.001x)

Where, p is the price of the product in dollars and x is the number of units sold. Also verify the result using technology.

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