# 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

## Stephen F. Austin State University

**Formulas Key:**

Blue: Linear

Green: Cubic

Purple: Exponential

## University of Arkansas at Fayetteville

Formulas Key:

Red: Linear

Blue: Cubic

Green: Exponential

## 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.

**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?

## SFA: Tuition Costs from 50 years ago

## 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.