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 2.1, Problem 78E

(a)

To determine

To find: The expression according piecewise defined expression.

Expert Solution

Answer to Problem 78E

The complete expressions is T(x)={75xif 0x2150+50(x2)if x>2 .

Explanation of Solution

The hotel chain charges $75 each night for the first two nights and $50 for each additional night’s stay,

Let x be the number of nights.

The charges for two days or less is,

T(x)=75x

The charges for more than two days is,

T(x)=150+(50x)

Thus, the complete expressions is T(x)={75xif0x2150+50(x2)ifx>2 .

(b)

To determine

To find: The value of expression T(x) at given nights.

Expert Solution

Answer to Problem 78E

Hotel chain charges at T(2) is $150 , at T(3) is $200 and at T(5) is $300 .

Explanation of Solution

Given:

The expression is,

T(x)={75xif0x2150+50(x2)ifx>2

Calculation:

The given expression is,

T(x)={75if0x2150+50xifx>2

Expression for two nights is,

T(x)=75x

Substitute 2 for x in the above expression to find the value of T(2) ,

T(x)=75×2=$150

So, hotel chain charges at T(2) is $150 .

Expressionof charges for more than two nights is,

T(x)=150+50(x2) (1)

Substitute 3 for x in equation (1) to find the value of T(3) ,

T(x)=150+50(32)=150+50×1=$200

So, hotel chain charges at T(3) is $200 .

Substitute 5 for x in equation (1) to find the value of T(5) ,

T(x)=150+50(52)=$300

So, hotel chain charges at T(5) is $300 .

Thus, hotel chain charges at T(2) is $150 , at T(3) is $200 and at T(5) is $300 .

(c)

To determine

To explain: The resultant of given function at certain values mentioned in part (b).

Expert Solution

Answer to Problem 78E

This represents the total cost of staying at the hotel.

Explanation of Solution

From part (b),

Hotel chain charges at T(2) is $150 , at T(3) is $200 and at T(5) is $300 .

This represents the total cost of staying at the hotel.

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