Predicting MTA Fare Trends in NYC: Linear Modeling Analysis
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CUNY LaGuardia Community College *
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Course
115
Subject
Mathematics
Date
Jun 9, 2024
Type
docx
Pages
8
Uploaded by DrRedPandaPerson1011
Name: Rozan Alias
Project: Linear Modeling (PQL) Mat 115:Prof. Rudy Meangru Project #1: ( / 30 pts) 2- week period [ Dear student you may consult with other students for help, but under no circumstances take someonelse work and claim it to be yours
] In this activity you will be investigating the rising cost of the MTA transit fare over a period of time in New York City. The goal is to use data to develop a simple mathematical model which can be used to make some reasonable predictions. You will incorporate the use of algebraic skills such as graphing, rate of change and linear function to complete this activity. Step 1: Introduction ( 2pts)
Read through this activity and then write a brief introduction
of the goals
in this activity. -
The goals in this activity is :
Create scatter plot for the data to determine if the trend of the date linear
Determine the input and the output values
Convert the data to two coordinate pairs and find the intercepts and the slope to build the model
Use the model to make a predictions Step 2: Scatter Plot ( 5pts)
Use the following data provided in the table below to obtain a scatter plot
of time vs. price. Describe
the trend of the price in the plot. Do you find the trend shocking? Time Line Price(dollars) 1970 $0.20 1980 $0.50 2003 $2.00 2009 $2.25 2013 $2.50 2015 $2.75 1
1960
1970
1980
1990
2000
2010
2020
0
0.5
1
1.5
2
2.5
3
the difference between the raising in the fare in the 2000’s and in the 90’s was shocking for me even if it make sense in the real world but I never knew that one day the MTA fare
was 0.30$ 😊
Step 3: Defining your variables
.(2 pts) Identify your independent and dependent variables
using appropriate symbols to state them. Let the independent variable ?? represents the time in years and the dependent variable ?? represents the cost in dollars. Independent variables (time/years)
(t) 1970
1980
2003
2009
2013
2015
dependent variables (cost/dollar)
(f(t))
0.2
0.5
2
2.25
2.5
2.75
2
Step 4: Average rate of Change (4 pts)
Compute the average rate of change
per year of the cost over each time
period. Just fill in the result; don’t’ show the calculation. Time Line Price(dollars) Average rate of change 1970 $0.20 XXXXXXXXXXXXX 1980 $0.50 0.03/year
2003 $2.00 0.065/year 2009 $2.25 0.4/year 2013 $2.50 0.0625/year 2015 $2.75 0.125/year Do these values suggest a linear trend? Explain. Yes they do, we can see from the trend in the data that the cost of the MTA fare increase as the time increase.
Step 5: Linear Modeling
(6 pts) Assuming that the trend is linear, generate a linear model. To make the calculation easier, rescale the time values
for 2009 through 2015 in the above table. Let 2009 be the year 0.
t P( dollars) 0 2.25
1
2.3125
2
2.375
3
2.4375
4
2.5
5
2.5625
6
2.75 Using any two data points from the rescaled table develop a possible
linear model of the above data
by filling in the blanks in the following calculation. 3
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