2: Your job pays you $8.50 an hour for a normal 40 hour work week. Create a piecewise function to model the parking fees.Įx. A flat rate of $13 plus $3 per hour for each hour after 2 hours. A flat rate of $12.50 for any amount of time over 1 hour and up to and including 2 hours. 1: A city parking lot uses the following rules to calculate parking fees: A flat rate of $5.00 for any amount of time up to and including the first hour. b) How many kilowatt-hours were used if a monthly electric bill was $57.06?ġ6 Solution: Example 5 h = # kilowatt-hoursĬ(h) = Cost of total kilowatt-hours b) KwhĮx. a) Create a function to model this scenario. The company charges $0.11 per kilowatt-hour for all electrical usage in excess of 200 kWh. Southeast Electric charges $0.09 per kilowatt-hour for the first 200 kWh. $25.50 = hourly pay hours in excess of 40 h = # of hours worked h-40 =# hours worked in excess of 40 P(h) = total amount of paycheck b) 8.5 overtime hoursġ5 Example 5: Create a Piecewise Function b) One week she earned $ How much overtime did she work?ġ4 Solution: Example 4 $17 = hourly pay: hours up to 40. Create a function to represent the amount of her paycheck. t = number of text messages sent T-500 = number of texts in excess of 500 allotted C(t) = Cost of your cell phone bill b) $100ġ3 Example 4: Create a Piecewise FunctionĪ construction worker earns $17 per hour for the first 40 hours of work and $ per hour for work in excess of 40 hours. $0.10 = cost of each text in excess of the plan’s allotted 500. b) How much will it cost you if you send 750 text messages?ġ2 Solution: Example 3 $75 = monthly cost of cell phone bill a) Write a piecewise function to determine the amount of your cell phone bill. It costs $0.10 per text message sent in excess of the 500 that you are originally allotted. P(c) = the price of all cups ordered $1.40 cost of each cup if 20 or less are ordered $12.00 shipping if 20 or less are ordered $1.10 cost of each cup if more than 20 are ordered $15.00 shipping if more than 20 are ordered b) $34.40 c) 27 cupsġ1 Example 3: Create a Piecewise FunctionĮvery month your cell phone plan costs $75 and gives you unlimited talk, 500 text messages, and no data plan. Create a function to describe the price of cups.ī) How much will it cost the Mad Hatter to order 16 cups? c) If the Mad Hatter wants to spend at most $45, what is the maximum number of cups he can order?ġ0 Solution: Example 2 c = the number of cups ordered For orders of more than 20 cups, the price is $1.10 per cup plus $15 shipping and handling. For orders of 20 or fewer cups, the price is $1.40 per cup plus $12 shipping and handling on the order. The Teacups, Limited catalog prices cups according to the number of cups ordered. The Mad Hatter is ordering cups from Teacups, Limited, for his tea party. Create a piecewise function to represent the cost of the bags of snickers.ħ Solution: Example 1 b = number of bags of snickersĬ(b) = Cost of all bags of snickers purchased $3.45 = cost of a bag if less than 4 bags are purchased $3.00 = cost of a bag if 4 or more bags are purchased. A bag of snickers costs $3.45, but if you buy 4 or more bags, they only cost $3.00per bag. You decide to buy snickers because they have a special deal on snickers. b) Does your answer make sense in the context of the problem? STEP 4: Check Your Work: a) Check the solution in the original equation. STEP 3: Execute the Plan: a) Model the problem with the equation. d) Relate the given info to the unknown info with a formula or equation. c) Define the variable using the unknown info. STEP 2: Devise a Plan: a) Highlight any given information. STEP 1: Understand the problem: a) Read the entire problem. Today’s objective: I can write a piecewise function from multiple representations. \(y_i=\beta_0 \beta_1x_ x_2\) as the predictors.1 Creating Piecewise Functions from Real World Scenarios – Day 3 So, let's formulate a piecewise linear regression model for these data, in which there are two pieces connected at x = 70: As you can see, the estimated two-piece function, connected at 70% -the dashed line -appears to do a much better job of describing the trend in the data. We could instead split our original scatter plot into two pieces -where the water-cement ratio is 70% -and fit two separate, but connected lines, one for each piece. Provides yet more evidence that our model needs work.
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