   Chapter 5.2, Problem 54E ### 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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# Supply In Exercises 53 and 54, find the supply function x   =   f ( p ) that satisfies the initial condition. d x d p  =  10 P   −   3 x  = 100 when  p   =   $3 To determine To calculate: The supply function x=f(p) for which dxdp=10p3 that satisfies the initial Condition x=100 when p=$3.

Explanation

Given Information:

The provided equation of derivative of the supply function is dxdp=10p3 and the initial

Condition is x=100, when p=\$3.

Formula Used:

According to the general power rule for integration,

If u is a differentiable function of x, then

undu=un+1n+1+C

Where n1

Calculation:

Consider the equation dxdp=10p3.

Integrate dxdp to obtain x.

x=10p3dp=10(p3)12dp

Apply the general power rule for integrtion in the above equation

x=10((p3)12+112+1)+C=10

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