1. 4.5 Writing a Function Rule Function Rule: An equation that describes a function.

2. GOAL:

3. In math problems many times we can look at what is happening to the data and see patterns. These patterns will provide the details to write Function Rules – equation. Ex: A landfill has 50,000 tons of waste in it. Each month it accumulates an average of 420 tons of waste. What is a function rule that represents the total amount of waste after m months?

4. To solve this problem, we must write down what we are given: A landfill has 50,000 tons of waste in it. Each month it accumulates an average of 420 tons of waste. What is a function rule that represents the total amount of waste after m months? Given: 1) 50,000 tons on the property already 2) 420 tons accumulate each month 3) m months after Define: Use a variable to represent the Final/Total amount. Here let W represent the total amount of waste. Write: Use the given info and the variable to write the Function Rule: W(m) = 420m + 50,000

5. YOU TRY IT: At a concert hall the mezzanine of 10 rows with 12 seats each at $25 is sold out. The revenue from ticket sales will depend on the number of general seating tickets sold. If the general seating has 30 rows with 16 seats which cost $10.00 each, What is the maximum possible total revenue?

6. YOU TRY IT: (Solution) Given: 1) Mezzanine: 10 rows, 12 seats each, $25.00 2) General: 30 rows, 16 seats, $10.00 Define: Let R be the total revenue Let n be the total general tickets sold Write: R = 10n + (10∙12∙25) At a concert hall the mezzanine of 10 rows with 12 seats each at $25 is sold out. The revenue from ticket sales will depend on the number of general seating tickets sold. If the general seating has 30 rows with 16 seats which cost $10.00 each, What is the maximum possible total revenue? General Seating revenueMezzanine revenue

7. YOU TRY IT: Carolyn has 420 CDs in her collection. Each month she adds 12 CDs to the collection. What equation is a Function Rule that represents Carolyn’s situation?

8. YOU TRY IT: (Solution) Given: 1) 420 CDs in collection already 2) 12 CDs each month added Define: Let Y be the total CDs Let x be the months after the 420 CDs Write: Y = 12x + 420 Carolyn has 420 CDs in her collection. Each month she adds 12 CDs to he collection. What equation is a Function Rule that represents Carolyn’s situation? CDs per month CDs already in the collection

9. VIDEOS: Functions https://www.khanacademy.org/math/algebra/rati o-proportion-topic/ratios_algebra/v/find-an- unknown-in-a-proportion https://www.khanacademy.org/math/algebra/rati o-proportion-topic/ratios_algebra/v/writing- proportions

10. CLASS WORK: Pages: 264 – 267 Problems: As many as it takes to master the concept.