# The expression according piecewise defined expression.

### Precalculus: Mathematics for Calcu...

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

### 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

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

Expert Solution

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

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.

### Have a homework question?

Subscribe to bartleby learn! Ask subject matter experts 30 homework questions each month. Plus, you’ll have access to millions of step-by-step textbook answers!