(3) Using your calculator, find the exact balance on the Pay-Per-Ride MetroCard mentioned above and use it to calculate the remaining balance after 0, 1, 2, 3 rides. Record your results in the table below. Amount Number remaining on of Rides Your calculations the card (R) (n) 0 1 2 3 (4) Construct a linear model with R representing the remaining amount of money on this Pay- Per-Ride MetroCard after each ride. R = (5) Using the model obtained in the previous question, fill out the table below. Number of Rides Amount remaining on the card (R) (n) 0 5 10 15 20 30 40 50(8) Review the characteristics that all linear models share and write them in the space below. Mathematical Terms of Characteristics of Linear Relationships Use the mathematical terms discussed above to answer the following questions. (a) What is the rate of change for the model? What does it mean in the context of the problem situation? Be sure to include units. (b) Indicate on your graph one of the vertical intercepts. What is the meaning of it in the context of the problem situation? (c) Does the model have a horizontal intercept? If so, circle the horizontal intercept and explain the meaning of it in the context of the problem situation? (9) Explain how you can tell from a graph if a linear model has a negative slope, positive slope, or slope of 0, Include sketches of each type of the graph. Positive Slope Negative Slope Slope of O . A positive Slope . A negative Slope HH moves upward on a graph moves downward on . slope of O means from left to right a graph from left the line is horizontal and the y- value stays to right the same as the X-value increasesPROBLEM SITUATION 3: METROCARD You have two options when purchasing a MetroCard in New York City. Your first option is to buy an unlimited MetroCard, where you buy an unlimited number of subway and bus rides for a flat rate price. You can choose between either a 7-Day or a 30-Day unlimited MetroCard. Currently, the cost of a 7-Day unlimited MetroCard is $31, while the 30-Day unlimited MetroCard is $116.50. Your other option is to buy a regular, Pay-Per-Ride MetroCard, where you can purchase a MetroCard for as many rides as you want. In 2015 the fare for subway or local bus ride was $2.75. If you buy a regular MetroCard and put at least $5.50 on the card, then you automatically get an 11% bonus added onto the MetroCard. In addition to the amount of money you decide to spend on either the unlimited or regular MetroCard, there is also a charge of $1.00 for the purchase of any new MetroCard. Fortunately, by refilling and reusing MetroCard your current MetroCard, you can avoid this additional fee. Francisco usually buys an unlimited MetroCard each month. However, his friend Manjula says that he doesn't take the subway enough to justify an unlimited ride MetroCard. Francisco takes the subway to work and back each weekday. He also takes the bus out to visit his parents every Sunday, but his Dad usually drives him back to his apartment in the city. One way to decide if Pay-Per-Ride MetroCard is a better deal is to consider Francisco spending the cost of the Unlimited MetroCard on a Pay-Per-Ride MetroCard and determine if it would last him for 30 Days. (1) Without using your calculator, estimate the balance on the Pay-Per-Ride MetroCard if Francisco deposits $116.50 onto it (HINT: You get a bonus when you purchase Pay-Per-Ride MetroCard. Also assume Francisco is reusing his old MetroCard to avoid $1 fee) (2) Estimate if this MetroCard would last Francisco 30 days (HINT: On average, there are 22 weekdays in any period of 30 days) 3 http://web.mta.info/Metrocard/mcgtreng.htm(6) Graph the data from table above. Be sure to include scales and label axes. Let the horizontal axis represent the number of rides and the vertical axis represent the amount of money remaining on the card. (7) Will the card last for the period of 30 days? What MetroCard would you suggest Francisco to buy? Explain your