Algebra and Trigonometry (6th Edition)
Algebra and Trigonometry (6th Edition)
6th Edition
ISBN: 9780134463216
Author: Robert F. Blitzer
Publisher: PEARSON
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**Title: Understanding Linear Function Models for Tennis Club Payment Options** A tennis club offers two payment options. Members can either pay a monthly fee of $30 plus $7 per hour for court rental time, or opt for a plan with no monthly fee where court time costs $9.50 per hour. Answer parts a through d. **a. Writing Linear Function Models** 1. **First Payment Option**: - Monthly fee: $30 - Hourly rate: $7 per hour **Linear Function**: Let \( x \) be the number of hours of court rental. The function to model the total monthly cost is: \[ f(x) = 30 + 7x \] 2. **Second Payment Option**: - No monthly fee - Hourly rate: $9.50 per hour **Linear Function**: The function to model the total monthly cost is: \[ f(x) = 9.5x \] **b. Using Graphing Utility** Use a graphing utility to plot the two functions within the interval \([0, 15]\) for the x-axis (hours) and \([0, 120]\) for the y-axis (total cost in dollars). Choose the correct graph that represents these functions. **c. Finding Intersection Points** Utilize your graphing tool’s trace or intersection feature to identify the point of intersection between the two graphs. This point represents the number of hours at which both payment options result in the same total monthly cost. **Graph Descriptions:** - **Option A**: A graph with two intersecting lines. - **Option B, C, D**: Graphs with lines having different slopes, indicating different cost models over time. Upon selecting the correct graph, you will determine the specific intersection point and its practical significance. **Conclusion:** If two graphs intersect at a point, it means at this specific number of rental hours, both payment options will cost the same. Understanding the graph intersection helps members decide which payment plan is more economical based on their expected court usage.
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Transcribed Image Text:**Title: Understanding Linear Function Models for Tennis Club Payment Options** A tennis club offers two payment options. Members can either pay a monthly fee of $30 plus $7 per hour for court rental time, or opt for a plan with no monthly fee where court time costs $9.50 per hour. Answer parts a through d. **a. Writing Linear Function Models** 1. **First Payment Option**: - Monthly fee: $30 - Hourly rate: $7 per hour **Linear Function**: Let \( x \) be the number of hours of court rental. The function to model the total monthly cost is: \[ f(x) = 30 + 7x \] 2. **Second Payment Option**: - No monthly fee - Hourly rate: $9.50 per hour **Linear Function**: The function to model the total monthly cost is: \[ f(x) = 9.5x \] **b. Using Graphing Utility** Use a graphing utility to plot the two functions within the interval \([0, 15]\) for the x-axis (hours) and \([0, 120]\) for the y-axis (total cost in dollars). Choose the correct graph that represents these functions. **c. Finding Intersection Points** Utilize your graphing tool’s trace or intersection feature to identify the point of intersection between the two graphs. This point represents the number of hours at which both payment options result in the same total monthly cost. **Graph Descriptions:** - **Option A**: A graph with two intersecting lines. - **Option B, C, D**: Graphs with lines having different slopes, indicating different cost models over time. Upon selecting the correct graph, you will determine the specific intersection point and its practical significance. **Conclusion:** If two graphs intersect at a point, it means at this specific number of rental hours, both payment options will cost the same. Understanding the graph intersection helps members decide which payment plan is more economical based on their expected court usage.
### Payment Options for Tennis Club Court Rentals A tennis club offers two payment options for their members regarding court rental time: 1. **Option 1**: Pay a monthly fee of $30 plus $3 per hour for court rental time. 2. **Option 2**: No monthly fee, but court time costs $9.50 per hour. #### Analysis of Costs **Task (c):** Use your utility's trace or intersection feature to determine where the two graphs intersect. Describe what the coordinates of this intersection point represent in practical terms. - **Intersection Point of Graphs**: (____, ____) - *(Type an ordered pair)* **Interpretation of Intersection Coordinates:** Select the correct choice below and fill in the answer box(es) to complete your choice. - **Option A**: For ____ hour(s), the cost of both plans is $____. - *(Type whole numbers)* - **Option B**: The cost of both plans will always be $____ and it will not depend on the number of rented hours. - *(Type a whole number)* - **Option C**: For ____ hour(s), the cost of both plans are different. The cost of the first plan is $____ and the cost of the second plan is $____. - *(Type whole numbers)* **Task (d):** Verify part (c) using an algebraic approach by setting the two functions equal to each other and determining how many hours one has to rent the court so that the two plans result in identical monthly costs. - Thus, one has to rent the court for ____ hour(s) so that the two plans result in identical monthly costs. - *(Type a whole number)* --- **Note:** The analysis should involve calculating the cost for each plan based on different scenarios and determining the number of hours where costs are equivalent, both graphically and algebraically.
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Transcribed Image Text:### Payment Options for Tennis Club Court Rentals A tennis club offers two payment options for their members regarding court rental time: 1. **Option 1**: Pay a monthly fee of $30 plus $3 per hour for court rental time. 2. **Option 2**: No monthly fee, but court time costs $9.50 per hour. #### Analysis of Costs **Task (c):** Use your utility's trace or intersection feature to determine where the two graphs intersect. Describe what the coordinates of this intersection point represent in practical terms. - **Intersection Point of Graphs**: (____, ____) - *(Type an ordered pair)* **Interpretation of Intersection Coordinates:** Select the correct choice below and fill in the answer box(es) to complete your choice. - **Option A**: For ____ hour(s), the cost of both plans is $____. - *(Type whole numbers)* - **Option B**: The cost of both plans will always be $____ and it will not depend on the number of rented hours. - *(Type a whole number)* - **Option C**: For ____ hour(s), the cost of both plans are different. The cost of the first plan is $____ and the cost of the second plan is $____. - *(Type whole numbers)* **Task (d):** Verify part (c) using an algebraic approach by setting the two functions equal to each other and determining how many hours one has to rent the court so that the two plans result in identical monthly costs. - Thus, one has to rent the court for ____ hour(s) so that the two plans result in identical monthly costs. - *(Type a whole number)* --- **Note:** The analysis should involve calculating the cost for each plan based on different scenarios and determining the number of hours where costs are equivalent, both graphically and algebraically.
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