BuyFind

Precalculus: Mathematics for Calcu...

6th Edition
Stewart + 5 others
Publisher: Cengage Learning
ISBN: 9780840068071
BuyFind

Precalculus: Mathematics for Calcu...

6th Edition
Stewart + 5 others
Publisher: Cengage Learning
ISBN: 9780840068071

Solutions

Chapter 3.1, Problem 67E
To determine

To evaluate: The number of times viewer watch it.

Expert Solution

Answer to Problem 67E

The numbers of viewer watch it is 30times .

Explanation of Solution

Given:

The effectiveness of a television is given by the function E(n)=23n190n2 , where n is the numbers of times viewer watch it.

Calculation:

The effectiveness of a television is given by,

E(n)=23n190n2=190n2+23n (1)

The standard form of function,

f(n)=an2+bn+c (2)

The maximum or minimum value of the function occurs at,

n=b2a (3)

If a>0 , then the minimum value is f(b2a) .

If a<0 , then the maximum value is f(b2a) .

From the equation (1) and (2),

a=190b=23

Substitute 190 for a and 23 for b in the equation (3),

n=232×190=23290[abcd=ab×dc]=23×902=30

The numbers of viewer watch it is 30times .

The function has maximum value,

a=190<0 .

Thus, the numbers of viewer watch it is 30times .

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