2.4 Linear Functions and Models I have dreams of orca whales and owls, but I wake up in fear. -Regina Spektor

Linear Model Applications A linear function is of the form Suppose that a company just purchased a fleet of new cars for its sales force at a cost of $28,000 per car. The company chooses to depreciate each vehicle using the straight-line method over 7 years. This means that each car will depreciate by $4000 per year. This can be represented by the following function: Where x represents number of years. Graph the linear function (window 0≤𝑦≤30000, 0≤𝑥≤10) b) Find the book value of each car after 3 years._________ c) When will the book value of each car be $8000? (show work) With the graph showing: 2nd  CALC (above TRACE)Value enter value for x  ENTER

Linear Model Applications The quantity of a good is the amount of a product that a company is willing to make available for sale at a given price. The quantity demanded of a good is the amount of a product that consumers are willing to purchase at a given price. Suppose that the quantity supplied, S, and the quantity demanded, D, of cell phones each month are given by the following functions: a) Graph the functions on the same graph (window 0≤𝑥≤100, 0≤𝑦≤3500). Sketch the graph. 𝑺 𝒑 =𝟔𝟎𝒑−𝟗𝟎𝟎 𝑫(𝒑)=−𝟏𝟓𝒑+𝟐𝟖𝟓𝟎

Linear Model Applications b) Find the equilibrium price – the price at which the quantity supplied equals the quantity demanded. ___________ What is the amount supplied at the equilibrium price? ___________ Label the equilibrium price and quantity on your graph. c) Determine the prices for which quantity supplied is greater than quantity demanded. (Show work) With the graph showing: 2nd  CALC (above TRACE)  Intersect  Enter, Enter, Enter

Linear Model Applications In baseball, the on-base percentage for a team represents the percentage of time that the players safely reach base. The data given in the table represent the number of runs scored, y, and the on-base percentages, x, for teams in the National League during the 2003 baseball season. Team On-Base Percent. Runs Scored Atlanta 34.9 907 St. Louis 35.0 876 Colorado 34.4 853 Houston 33.6 805 Phili. 34.3 791 San Fran. 33.8 755 Pittsburgh 753 Florida 33.3 751 Team On-Base Percent. Runs Scored Chic. Cubs 32.3 724 Arizona 33.0 717 Milwaukee 32.9 714 Montreal 32.6 711 Cincinnati 31.8 694 San Diego 33.3 678 NY Mets 31.4 642 Los Angeles 30.3 574

Linear Model Applications a) Use your graphing calculator to create a scatter plot of the data. b) Find the equation for the line of best fit: ________________________ Enter the data: STAT  Edit (make sure the lists are cleared before you start) Type in your data into each list. Use arrow keys to move between lists Create the scatterplot: Hit Y=  use arrows to highlight ‘Plot1’  ENTER Hit ZOOM  9 Choose a linear regression model: STAT  arrow over to highlight CALC  option 4 (LinReg)  ENTER Use the data the calculator gave you to put the equation into slope-intercept form (y = mx+b) Graph the line of best fit VARS  option 5 (Statistics)  arrow over to highlight EQ  option 1 (RegEQ) Hit ZOOM  9

Linear Model Applications c) If a team had an on-base percentage of 34.0, predict the number of runs they scored during the season. _______________ d) If a team scores 760 runs in a season, what might have been their on-base percentage? (show work) With the graph showing: 2nd  CALC (above TRACE)  option 1 (value) Enter in the value for x, hit ENTER

2.4 Linear Functions and Models Homework #20: p. 103 #31-39 odd, 51-55 odd I have dreams of orca whales and owls, but I wake up in fear. -Regina Spektor