   Chapter 7.4, Problem 67E ### 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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# Expenditures The expenditures z (in billions of dollars) for spectator sports from 2008 through 2013 can be modeled by z = 0.391 x − 0.069 y + 6 Where x is the expenditures (in billions of dollars) on amusement parks and campgrounds, and y is the expenditures (in billions of dollars) on live entertainment (excluding sports). (Source: U.S. Bureau of Economic Analysis)Find ∂ z / ∂ x and ∂ z / ∂ y .Interpret the partial derivatives in the context of the problem.

(a)

To determine

To calculate: The value of zx and zy from the expenditure function that is modelled by z=0.391x0.069y+6 for the spectator sports from 2008 through 2013.

Explanation

Given information:

The provided expenditure function z=0.391x0.069y+6 for the spectator sports from 2008 through 2013. Where, x is the expenditure on amusement parks and campgrounds and y is the expenditures on live entertainment.

Formula used:

Consider the function z=f(x,y) then for the value of zx consider y to be constant and differentiate with respect to x and the value of zy consider x to be constant and differentiate with respect to y.

Calculation:

Consider the provided function is,

z=0.391x0.069y+6

Partially derivative of the function z=0.391x0.069y+6 with respect to x.

zx=x(0.391x0.069y+6)=0.391x(x)0.069yx(1)+x(6)=0

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