College Cost Project

By Amanda Underwood and Ayoung Jo

College Choices

Public in-state school: Stephen F. Austin State University

Out of state school: The University of Arkansas at Fayetteville

Part A: Research and Function Writing

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Stephen F. Austin State University

Formulas Key:

Blue: Linear

Green: Cubic

Purple: Exponential



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University of Arkansas at Fayetteville

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Formulas Key:

Red: Linear

Blue: Cubic

Green: Exponential

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Part B: Mathematical Analysis

SFA: Predicted Prices of Tuition

1990-1991:

  • Linear: $-1007.68

  • Cubic: $17317.61

  • Exponential: $1439

2014-2015:

  • Linear: $8878.79

  • Cubic:$5107.20

  • Exponential: $10546

2018-2019:

  • Linear: $10526.54

  • Cubic: $-2179.95

  • Exponential: $14697.75

2040-2041:

  • Linear:$19589.14

  • Cubic: $-245204.59

  • Exponential: $91240.15

Arkansas: Predicted Price of Tuition

1990-1991:

  • Linear: $5775.55

  • Cubic:$20478.46

  • Exponential:$7523.02

2014-2015:

  • Linear:$18349.80

  • Cubic:$14088.15

  • Exponential:$19229.67

2018-2019:

  • Linear:$20445.51

  • Cubic:$6947.84

  • Exponential:$22484.10

2040-2041:

  • Linear:$31971.91

  • Cubic:$-226812.21

  • Exponential:$53145.84

SFA: Actual Tuition

1990-1991:$1622

2014-2015: $8772

Arkansas: Actual Tuition

1990-1991:$7040

2014-2015:$20336

SFA: Percent Error

1990-1991:

  • Linear: 162.13%

  • Cubic: 967.67%

  • Exponential: 11.28%

2014-2015:

  • Linear: 1.21%

  • Cubic: 41.78%

  • Exponential: 20.22%

Arkansas: Percent Error

1990-1991:

  • Linear:17.96%

  • Cubic:190.89%

  • Exponential: 6.86%

2014-2015:

  • Linear: 9.77%

  • Cubic: 31.12%

  • Exponential: 5.44%

Best Model Function?

Overall, the exponential function best modeled the cost of tuition for Stephen F. Austin University. For 1990-1991 tuition, exponential model was the only one that showed a percent change that was less than 100% (it was 11.28%) - the linear model showed a negative tuition fee (because the graph of it is just a straight diagonal line going up), and the cubic model had a crazy high number (for its graph, the y values went up and down as x increased). As for the 2014-2015 tuition, the linear model may have had the closest (smallest percent error) just for that year, but the cubic function (which had a percent error of 20.22%) still made for a plausible model.

Like for SFA University, the exponential function best modeled the cost of tuition for University of Arkansas Fayetteville. It showed the smallest percent error between calculated value and actual tuition for both 1990-1991 tuition and 2014-2015 tuition. (6.86% and 5.44%, respectively - which are very small values)

Consistently Better Model?

There was no consistent model that showed correlation to the tuition costs of the colleges. For example, the linear model for SFA showed a huge percentage error of 162.13% for 1990-1991, and then a small percentage error of 1.21% for 2014-2015. Also, the cubic models (for both colleges) showed great inconsistency, because cubic graphs fluctuate (y values (cost of tuition) move up and down as x values (years) progressively increases.). So, the cubic cube gave extremely unlikely costs (too high or too low (even into the negatives)). Exponential model (probably better than the other two) best modeled the tuition fees for much of the time, except when the years got too big. For example, according to the exponential model students would have to pay $91240.15 to go to SFA in 2040-2041 school year, which seems rather unlikely.

SFA: Tuition Costs from 50 years ago

$940
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Explanation

The graph including the tuition from 1964 is different of that of the one including just the tuition from 1990-2010 because in the original graph the values for the tuition were only mildly different, whereas the value for the tuition in 1964 is drastically different. Therefore the graph of the function will fluctuate more including the value for 1964.

Arkansas: Tuition costs 50 years ago

$8,670
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Explanation

Adding the tuition cost to go to Arkansas out of state in 1964 caused the graph of the original function to fluctuate. The cost of going out of state to college is significantly high, and the price to go out of state in 1964 was significantly lower, much lower than that of SFA. Lower in that the margin between the highest value and lowest value of Arkansas is much greater than SFA, which leads to the graph being even more indecisive in nature.

Reflection

This project on calculating the costs of tuition and how they would fluctuate throughout the years by using regressions has opened our eyes to how expensive college is. This project has influenced our own take on finding the right college for us, because money is always a large consideration in deciding where you want to spend your next four years. Also, looking into these two colleges, we saw things other than their tuition prices, like pictures of their campus, and other things. This allowed us to compare them with other colleges we've seen. I think this project was very interesting, and that instead of just giving us a word problem to find the regression, we were given a challenge that applied to what we are going through now, looking for the right college and what fits our financial state. We learned that you have to be conscious of the price of colleges and the fact that the cost of a college could be a deal breaker. We worked hard on this project because anything that challenges you academically and forces you to think about your future influences you in a positive way in the long run. In 40 weeks, 40 months, and 40 years, we'll remember that this project introduced us to the wonders of college, and taught us how to look for an ideal price for our education.