After a heavy rainstorm, Barbara's dog left muddy paw prints all over her back patio. She decided to rent an electric pressure washer to clean up the mess. The piecewise function below shows the rental charges for the pressure washer, dependent upon how many hours she rents it. Due to high demand, you cannot rent the washer for more than 24 hours at a time. Barbara's brother asked to use the washer and agreed to pay Barbara for any additional monies owed.
[tex]y=\left\{\begin{array}{l}26, 0 \\ 26+5(h-4), 4 \\ 60,8 \end{array}\right.[/tex]
If Barbara used the washer for 3 hours and her brother returned it to the store 7 hours after she rented it, how much does her brother owe her?
A. $15.00
B. $41.00
C. $60.00
D. $61.00
Answer (2)
Barbara's brother owes her $15 for the rental of the pressure washer. The total cost for 7 hours was $41, while Barbara's cost for 3 hours was $26. Subtracting these amounts gives $15.
;
Calculate the total rental cost for 7 hours using the piecewise function: $41 .
Calculate Barbara's rental cost for 3 hours using the piecewise function: $26 .
Subtract Barbara's cost from the total cost to find the amount her brother owes her: $41 − $26 = $15 .
Barbara's brother owes her $15 .
Explanation
Calculate the total rental cost for 7 hours First, we need to determine the total cost of renting the pressure washer for 7 hours. According to the piecewise function, if 4 < h ≤ 8 , the cost is given by y = 26 + 5 ( h − 4 ) . Since Barbara's brother returned the washer after 7 hours, we have h = 7 .
Calculate the total rental cost for 7 hours Now, we substitute h = 7 into the equation: y = 26 + 5 ( 7 − 4 ) y = 26 + 5 ( 3 ) y = 26 + 15 y = 41 So, the total rental cost for 7 hours is $$41.
Calculate Barbara's rental cost for 3 hours Next, we need to find out how much Barbara paid for using the washer for the first 3 hours. According to the piecewise function, if 0 < h ≤ 4 , the cost is $26. S in ce B a r ba r a u se d i t f or 3 h o u rs , w hi c h f a ll s in t hi sr an g e , h ercos t i s $26.
Calculate the amount her brother owes her To find out how much Barbara's brother owes her, we subtract Barbara's cost from the total cost: $41 − $26 = $15 Therefore, Barbara's brother owes her $$15.
Final Answer The amount Barbara's brother owes her is $$15.
Examples
Piecewise functions are useful in real life for modeling situations where different rules or costs apply over different intervals. For example, cell phone plans often have different rates for data usage depending on how much data you've used in a month. The first few gigabytes might be cheaper, but once you exceed that limit, the cost per gigabyte increases. Similarly, tiered pricing for electricity or water usage can be modeled using piecewise functions, where the price per unit changes as your consumption increases.
