Easy and fast Maths project

Project on Inquiry & Problem-Solving Competency

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Name:________________________________

Linear Modeling of NYC MTA Transit Fare Over Time Created by Prof Rudy Meangru

Mat 117, Section 3146 – Instructor Dr Gjoci Inquiry-Learning Project – 10% of your grade. Project Grading ____/ 30 pts total

The first version of it is due on Thursday, Nov 12. By November 18, the instructor will provide feedback/guidance for you to incorporate in your revision to write the final version of the project which is due on Nov 30th.

[Dear student you may consult with other students for help, but under no circumstances take someone else’s 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.

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?

Timeline Price(dollars) 1970 $0.20 1980 $0.50 2003 $2.00 2009 $2.25 2013 $2.50 2015 $2.75

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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.

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, no need to show the calculation.

Timeline Price(dollars) Average rate of change 1970 $0.20 1980 $0.50 2003 $2.00 2009 $2.25 2013 $2.50 2015 $2.75

Do these values suggest a linear trend? Explain.

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 4 2.50 6 2.75

Project on Inquiry & Problem-Solving Competency

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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.

(0, 2. 25) and ( 4 , 2.75 ) P = at + b P = at + ? a = ( - )/( - ) a = / a = P = ?t + ?

(a) Predict the price in 2021 For 2020, t = ? P = ?( ? ) + ? P = According to this model, the Price is expected to be about $ ______ in the year 2021. Step 6: Using EXCEL (6 pts)

(b) Obtain a scatter plot of the data with the “best-fit” line.

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(c) Generate the linear model through EXCEL.

(d) Using this model predict the price in 2021.

Step 7: Reflection ( 5 pts)

What have you learned from this activity? What challenges did you face and how did you overcome them? What mathematical skills and knowledge did you use to complete this assignment? Did you need to look back at any prior mathematical skills? Did you seek assistance from anyone and was it helpful? Compare the predictions that you get from the two models? Is your computed value a reasonable one to what the fare is currently? What are some of the pitfalls with this linear modeling procedure? Has this activity help you to better appreciate mathematics? How has this change your feeling about mathematics?

Project on Inquiry & Problem-Solving Competency

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Addendum

EXCEL INSTRUCTION

Let’s use the table below as a sample to obtain the desired out from EXCEL. Day Expense

1 30.80 2 25.55 3 26.35 4 28.30 5 30.50 6 50.50 7 60.80

Step 1: Access Excel spreadsheet.

Step 2: Enter the data set either my typing it in EXCEL or copy from the word file and paste it into EXCEL.

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Step 3: To obtain a scatterplot, highlight the data set, select “Insert” on the menu bar and then “Scatter” .

Step 4: Make a choice to obatin the scatter plot.

Step 5: To obtain a regression line or curve, place your cursor on any dot and right click. A pull-down menu appears. Select “ Add Threadline” and choose the required model anlong with “ Display Equation on chart”