   Chapter 11.1, Problem 92E Finite Mathematics and Applied Cal...

7th Edition
Stefan Waner + 1 other
ISBN: 9781337274203

Solutions

Chapter
Section Finite Mathematics and Applied Cal...

7th Edition
Stefan Waner + 1 other
ISBN: 9781337274203
Textbook Problem

Food versus Recreation The following equation shows the approximate relationship between the percentage y of total personal consumption spent on food and the corresponding percentage x spent on recreation. y = 688 x 1.99  percentage points   ( 4.83 ≤ x ≤ 9.35 ) According to the model, spending on food is decreasing at a rate of   _ _ _ _ _ percentage points per 1 percentage point increase in spending on recreation when 6.0% of total consumption is spent on recreation. (Your answer should be rounded to two significant digits.) [HINT: See Example 2(b).]

To determine

To fill: The following blank:

The rate of decrease of_____ percentage points per one percentage point increase in spending on recreation when 6.0% of total consumption is spent on recreation where the relation between percentage y of total consumption spent on food and the corresponding percentage x spent on recreation is given by y=688x1.99 percentage points. The range in which x lies is 4.83x9.35. Round the answer to two significant digits.

Explanation

Given Information:

Total consumption is spent on recreation is 6.0% where the relation between percentage y of total consumption spent on food and the corresponding percentage x spent on recreation is given by y=688x1.99 percentage points. The range in which x lies is 4.83x9.35.

Consider the function, y=688x1.99

Convert the function to power form,

y=688x1.99

Power rule of a function y=xn is dydx=nxn1, where n is some constant.

Constant multiple rules of derivative of a function f(x) are ddx[cf(x)]=cddx[f(x)] where c is constant.

Apply power rule and constant multiple rules of the derivative to the function,

dydx=688(1

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