Question

solve the problems.
1 lacey pays $15 for each hour of golf lessons and $10 for equipment rental. if a lesson is more than 3 hours long, she only pays $5 for equipment rental to the total cost of lacey’s lesson a function of the number of hours she used? use a table to help explain your answer. show your work.

Explanation:

Step1: Define the function for \( h \leq 3 \)

For \( h \leq 3 \) (where \( h \) is the number of hours), the cost of the lesson is \( \$15 \) per hour and equipment rental is \( \$10 \) per lesson. So the total cost \( C(h) \) is the sum of the lesson cost and equipment cost. The lesson cost for \( h \) hours is \( 15h \), and equipment cost is \( 10 \). So \( C(h)=15h + 10 \) for \( h = 1,2,3 \).

Step2: Define the function for \( h>3 \)

For \( h>3 \), the lesson cost is still \( \$15 \) per hour, but the equipment cost is \( \$5 \) per lesson. So the total cost \( C(h)=15h + 5 \) for \( h>3 \).

Step3: Create a table for \( h = 1,2,3,4,5 \)

Number of Hours (\( h \))	Lesson Cost (\( 15h \))	Equipment Cost	Total Cost (\( C(h) \))
2	\( 15\times2 = 30 \)	10	\( 30 + 10 = 40 \)
3	\( 15\times3 = 45 \)	10	\( 45 + 10 = 55 \)
4	\( 15\times4 = 60 \)	5	\( 60 + 5 = 65 \)
5	\( 15\times5 = 75 \)	5	\( 75 + 5 = 80 \)

Answer:

The total cost function is \( C(h)=

$$\begin{cases}15h + 10, & h\leq3 \\15h + 5, & h > 3\end{cases}$$

\) (where \( h \) is a positive integer representing hours), and the table is as shown above.