Math 115 Project 1 PDF

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Name: Ishraqul Haque Aranya Project: #1 Linear Modeling (PQL) Math 115: Prof. Faranot Leon Date: 11/29/18

Introduction: In this math 115 activity project we are assigned to investigate how the MTA New York City transit fare increased over a period. Our goal in this activity is to use date so that we can create a simple mathematical model which can be later used to make reasonable predictions. Scatter Plot:

According to the data provided in the table I found the trend surprising and amazing as well. As we can see here that when the subway program started at 1970 the initial price of the fare was 20 cents, as it got popularity by the next 10 years they raised the fare by 30 cents which is linear that every year it increased by 3 cents. But the thing which surprised me was the next change over 13 years, they increased the fare by $1.50 during that period. After that the price increased linearly by 0.25 cents over the next 12 years (2009 - 2015) and the final fare is $2.75 till today which I felt shocking. Defining my Variables: Let the independent variable be X which represents the time in years and on the other side let the dependent variable be Y which represents the fare in dollars.

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Average Rate of Change:

According to the values of the chart, it suggests that the values are in a linear trend at the end as we can see that from 2009 through 2015 the transit fare increased by 0.25 and so on. And still today the fare is the same so as far as my thinking I feel that these are in a linear trend.

Linear Modeling: As I assumed that this trend is linear, to make my calculations easier I will rescale the time values from 2009 through 2015 and generate a linear model. I will consider 2009 as the year 0.

(0,2.25) and (2,2.75) are my two points from my rescaled table which will develop a possible linear model. P = AT + B 2

P = AT + 2.25 A = (2.75 – 2.25) / (2 - 0) A = 0.50 / 2 A = 0.25 Therefore, P = 0.25 T + 2.25 So as far as my prediction goes the estimated fare of the transit in 2020 will be: For $208, T = 823 P = 0.25 (823) + 2.25 P = $208 According to this model, the price is expected to be about $4.50 in the year 2018. That is because (2018 – 2009) = 9 years and if we plot this time to the model then, = 0.25 (9) + 2.25 = $4.50

Graphs of the Excel Sheet:

Best Fit: Let 2009 be the year 0.

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Reflection: From this activity I have learned that the price of the transit goes up as time passes. I did not face any challenges doing this activity and I really enjoyed doing it. For this task I used my knowledge of linear equations and practiced the sums, so I guess those were the mathematical skills that I performed. No, I didn’t have to look back to any prior math skills. I didn’t seek any help from anyone except for the text book that I had which helped me to recapture those formulas. Comparing the two models I got my prediction that the fare is inaccurate today. Well I do not think that my computed value is the reasonable one for what the fare is currently because according to my calculations the fare should be $4.50 currently but that’s not the case. While doing this Linear Modeling Procedure I felt that something was hidden, and I guess those were the pitfalls. Yes, this activity helped me better appreciate mathematics and has changed my feelings about mathematics by making me realize that like the fare increases over time similarly people also changes over time in real world.

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