   Chapter 5, Problem 34RE ### Calculus: An Applied Approach (Min...

10th Edition
Ron Larson
ISBN: 9781305860919

#### Solutions

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

10th Edition
Ron Larson
ISBN: 9781305860919
Textbook Problem
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# Cost The marginal cost for a catering service to cater to x people can be modeled by d C d x = 20 x x 2 + 1000 . When x = 200, the cost C (in dollars) is $4049.69.Find the cost function.Find the costs of catering to 500 people and 1000 people. (a) To determine To calculate: The cost function for a catering service that can be modeled by dCdx=20xx2+1000. Explanation Given Information: The rate of change of the cost function with respect to people; dCdx=20xx2+1000. The initial condition C(200)=$4049.69

Here people is x and output (in hours) is C.

Formula used:

The power rule of integrals:

undu=un+1n+1+C (for n1)

Here, u is function of x.

The property of Intro-differential:

df(x)dxdx=f(x)

Calculation:

Consider the derivative:

dCdx=20xx2+1000

Apply, integration on both sides:

dCdxdx=20xx2+1000dx+C=10(x2+1000)

(b)

To determine

To calculate: The cost of catering to 500 people and 1000 people.

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