   Chapter 11.4, Problem 83E 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 Education The percentage y (of total personal consumption) an individual spends on food is approximately y = 35 x − 0.25  percentage points  ( 6.5 ≤ x ≤ 17.5 ) , where x is the percentage the individual spends on education. An individual finds that she is spending x = 7 + 0.2 t percent of her personal consumption on education, where t is time in months since January 1. Use direct substitution to express the percentage y as a function of time t (do not simplify the expression), and then use the chain rule to estimate how fast the percentage she spends on food is changing on November 1. Be sure to specify the units. [HINT: See Example 3(a).]

To determine

To calculate: The percentage y (of total personal consumption) a person spends on food as a function of time t by using direct substitution and the rate at which the percentage an individual spends on food is changing on November1 using chain rule if it is given that the percentage y(of total personal consumption) an individual spends on food is given by the equation y=35x0.25 percentage points (6.5x17.5), where x represents the percentage the individual spends on education and an individual finds expenditure percent of personal consumption on education given by the function x=7+0.2t where t is the time in months since January1.

Explanation

Given Information:

The percentage y(of total personal consumption) an individual spends on food is given by the function y=35x0.25 percentage points (6.5x17.5), where x represents the percentage the individual spends on education and an individual finds the expenditure percent of personal consumption on education is given by the equation x=7+0.2t where t is the time in months since January1.

Formula used:

Derivative of function f(x)=(u)n using chain rule is f'(x)=ddx(u)n=nun1dudx, where u is the function of x.

Calculation:

Consider the function, y=35x0.25

Directly substitute x=7+0.2t in the given function,

y=35(7+0.2t)0.25

Consider the function, y=35(7+0.2t)0.25

Apply the chain rule,

dydt=ddt35(7+0

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