Chapter 3: Exercises with Solutions

Elementary and Intermediate Algebra: Graphs & Models (3rd Edition)

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Section 3.1 Linear Models 233 Version: Fall 2007 3.1 Exercises 1. Jodiah is saving his money to buy a Playsta- tion 3 gaming system. He estimates that he will need $950 to buy the unit itself, accessories, and a few games. He has $600 saved right now, and he can rea- sonably put $60 into his savings at the end of each month. Since the amount of money saved de- pends on how many months have passed, choose time, in months, as your indepen- dent variable and place it on the hori- zontal axis. Let t represent the number of months passed, and make a mark for every month. Choose money saved, in dollars, as your dependent variable and place it on the vertical axis. Let A represent the amount saved in dollars. Since Jodiah saves $60 each month, it will be convenient to let each box represent $60. Copy the following coordinate system onto a sheet of graph paper. Copyrighted material. See: http://msenux.redwoods.edu/IntAlgText/ 1 Time t (months) Amount saved A (dollars) 0 2 4 6 60 180 300 420 540 660 780 900 1020 a) At month 0, Jodiah has $600 saved. This corresponds to the point (0 , 600) . Plot this point on your coordinate sys- tem. b) For the next month, he saved $60 more. Beginning at point (0 , 600) , move 1 month to the right and $60 up and plot a new data point. What are the coordinates of this point? c) Each time you go right 1 month, you must go up by $60 and plot a new data point. Repeat this process until you reach the edge of the coordinate system. d) Keeping in mind that we are mod- eling this discrete situation continu- ously, draw a line through your data points. e) Use your graph to estimate how much money Jodiah will have saved after 7 months. f) Using your graph, estimate how many months it will take him to have saved
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234 Chapter 3 Linear Functions Version: Fall 2007 up enough money to buy his gaming system, accessories, and games. 2. The sign above shows the prices for a taxi ride from Liberty Cab Company. Since the cost depends on the distance trav- eled, make the distance be the indepen- dent variable and place it on the hori- zontal axis. Let d represent the distance traveled, in miles. Because the cab com- pany charges per 1 / 6 mile, it is conve- nient to mark every 1 / 6 mile. Make price, in $, your dependent vari- able and place it on the vertical axis. Let C represent the cost, in $. Because the cost occurs in increments of 40 c , mark every 40 c along the vertical axis. Copy the following coordinate system onto a sheet of graph paper. distance d (miles) Cost C ($) 0 1 2 3 0 . 20 0 . 60 1 . 00 1 . 40 1 . 80 2 . 20 2 . 60 3 . 00 3 . 40 3 . 80 4 . 20 4 . 60 5 . 00 5 . 40 5 . 80 6 . 20 6 . 60 a) For the first 1 / 6 mile of travel, the cost is $2.30. This corresponds to the point ( 1 / 6 ,$2.30). Plot this point on your coordinate system. b) For the next 1 / 6 of a mile, the cost goes up by 40 c . Beginning at point ( 1 / 6 ,$2.30), move 1 / 6 of a mile to the right and 40 c up and plot a new data point. What are the coordinates of this point?
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