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Inquiry Problem Solving Competency

Analyze NYC MTA fare trends over time using linear modeling. Includes scatter plots, rate of change, and a linear function to predict future costs. A great project for exploring real-world applications of algebra and data interpretation.

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    1 M A I 115: Inquiry Problem Solving Competency MAT 115: College Algebra & Trigonometry Professor Mahdi Majidi-Zolbanin December b, 2024 2 Project One: Linear Modeling of NYC MTA Transit Fares Over Time Step 1: Introduction My goals for this activity will be co oversee the prices of rhe MTA fares throughout the years and to create a mathematical model in which can predict the future increases as well. Must include: - Graphs - Rate of Change - Linear Function Step 2: Scatter Plots Timeline Price (Dollars) 1970 50.20 1980 50.50 2003 52.00 2009 52.25 2013 52.50 2015 52.75

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    3 Price (Dollars) vs. Time Line 3 3 i Q 1970 1 9 M 1990 2000 2010 Tirtw bn» The trend of the chart was very low in the beginning however as the and seemed to have increased in increments of 10 cents. The jump between 1980 to 2003 will not be factored as the prices have also steadily increased but were not charted. 2003 through 2015, the fare has also increased (bv the given table) by 25 cents. P r i c e i Dcll-a i-s i Step 3: Defining M y Var iables Independent Variable- X - represents ± e time in years. Dependent Variable- ¥ - represents the cost in dollars.

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    4 Step 4: Average Rate of Change Timeline Price (Dollars) Average Rate of Change 1970 $0.20 xxxxxxxxxxxxx 1980 $0.50 0 0 3 2003 $2.00 0.15 2009 $2.25 0.25 2013 $2.50 0.25 2015 $2.75 0.25 These values do in fact represent a linear trend because the value has been proven to increase at a positive and constant rate. Thus far creating a linear trend that can be shown. Step 5: Linear Modeling Assuming chat the trend is linear, generate a linear model To malce the calculation easier, rescale rhe time values for 2009 through 2015 in the table below. t P (Dollars) 0 $2.25 1 $2.50 2 $2.75

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