# College Cost Project

### By: Nishali Naik and Veena Suthendran (4th period Wilt)

## Part A: Research and Function Writing

## Cost of Tuition from 2000 to 2010 where year 2000 x=0 for Brown University and University of North Texas

## Brown University linear, exponential, and cubic models

## Graph of All Functions for Brown University

Key

Red: Linear

Blue: Exponential

Green: Cubic

x=number of years from 2000

y=tuition ($)

Link to Desmos Graph: __https://www.desmos.com/calculator/3pozg3jewk__

## University of North Texas (UNT) linear, exponential, and cubic models

## Graph of All Functions for UNT

Key

Red: Linear

Blue: Exponential

Green: Cubic

x=number of years from 2000

y=tuition ($)

Link to Desmos Graph: __https://www.desmos.com/calculator/eyk0pgbrhh__

## Part B: Mathematical Analysis

## Predicted Tuition using Linear Model

## Predicted Tuition using Exponential Model

## Predicted Tuition using Cubic Model

## Actual Tuition for the schools in 1990-1991 and 2014-2015

__Actual Tuition__

**Brown**

1990-91: $20,720

__http://www.brown.edu/Administration/News_Bureau/1995-96/95-091.html__

2014-15: $62,694

__http://www.brown.edu/admission/undergraduate/apply-brown/tuition-and-aid__

**UNT**

1990-91: $3,326

__http://www.collegesimply.com/colleges/texas/university-of-north-texas/price/__

2014-15: $22,030

__http://financialaid.unt.edu/2014-2015-academic-year-traditional__

## Percent Error between calculated value and actual tuition cost

## Percent Error with Linear Model

## Percent Error with Exponential Model

## Percent Error with Cubic Model

## Function that best models the cost of tuition for each school

## One Model that was better consistently

We predicted that the exponential mathematical model would best represent the rise in tuition over the years, however our data did not agree. In regards to Brown University, the linear model was better consistently at predicting the tuition costs for a specific year. This is represented in the percent error which was derived by taking the predicted value and subtracting the exact value then dividing this all by the exact value. The linear model predicted that in 1990-1991 the tuition cost would be 24,692.41 while the actually cost was $20,720. The percent change between these two was about 19%. Between the years 2014-2015 the percent change was about 31%. However, when calculating the percent with the other functions such as with the exponential the percent change between the years 1990-1991 and 2014-2015 were 27% and 31% respectively. Additionally, the percent change between the same two time intervals in regards to the cubic function was about 73% and 23%. The data indicates that overall the linear model seems to show the least percent error, thus the linear model was better with Brown University. This is not the case with UNT (University of North Texas) because the percent error indicates that the exponential model showed the least percent error. During the same two time intervals as mentioned previously, the percent error for the exponential model was about 40% and 50% respectively. On the other hand, with the linear models the percent error was about 95% and 57%, while with the cubic function the percent error was about 356% and 66% respectively. There doesn't seem to be a consensus on the overall model which was consistently better when looking at both school, Brown University and the University of North Texas had different models which were better suited to predicting their tuition.

## Tuition 50 years ago

## UNT and Brown Tuition data with tuition from 1950; year 2000= 0

## Mathematical Models (Linear, Exponential, and Cubic) for Brown University and UNT including tuition 50 years ago

## Graph of all functions for Brown University including tuition in 1950

Key

Red: Linear

Blue: Exponential

Green: Cubic

x=number of years from 2000

y=tuition ($)

Link to Desmos Graph: https://www.desmos.com/calculator/wobq6ufkxx

## Graph of all functions for UNT including tuition in 1950

Key

Red: Linear

Blue: Exponential

Green: Cubic

x=number of years from 2000

y=tuition ($)

Link to Desmos Graph: https://www.desmos.com/calculator/lfe7zjm9qp