# College Financing

### Marianne Duer and Katrina Songco

Wilt 4th

# Stephen F. Austin University

**Part A: Research and Functions**

**Functions:**

**Graphs:**

**Part B: Mathematical Analysis**

Using the formulas above, the tuition costs were predicted for the years of 1990-1991, 2014-2015, 2018-2019 and 2040-2041

After researching the actual tuition costs for 1990 -1991 and 2014-2015, the percentage error was calculated using the following formula:

% Error = (|Estimated cost - Actual cost| / |Actual cost|) x 100

**3. Which function (linear, cubic, or exponential) best models the cost of tuition for each school? Why? **

The linear regression best models the cost of tuition for Stephen F. Austin University. This is because out of the three models, the linear function showed the least percent error regarding the actual cost of SFA's tuition. From the mathematical calculations, the linear function was most accurate in predicting the cost of tuition for the year 2014, only a 2.93% error. The other two models, displayed high percentages of error from the year 2014.

**4. Was one model (linear, cubic, or exponential) better consistently? Was this what you expected?**

The cubic model showed better consistency. When drawn a line on the regression, the line hits all of the points. This means, the function is closest to the tuitions

of Stephen F. Austin. I had expected the exponential growth function to show the most consistency because of the constant increase in tuition prices.

**5. Research the tuition cost from at least 50 years ago. Add this value to table and run another regression. How does this change things?**

In 1987, SFA's earliest year accounted for, the tuition cost was $850. When this value is added, the equations change as follow:

a. Linear - f(x)=290.724x+3442.884

b. Cubic - f(x)=-0.908x^3+13.028x^2+440.073x+2381.362

c. Exponential - f(x)=1806.862 (1.102)^x

# Franciscan University in Steubenville, OH

**Part A - Research and Functions**

**Functions:**

Graphs:

**Part B - Mathematical Analysis**

Using the formulas above, the tuition costs were predicted for the years of 1990-1991, 2014-2015, 2018-2019 and 2040-2041

After researching the actual tuition costs for 1990 -1991 and 2014-2015, the percentage error was calculated using the following formula:

% Error = (|Estimated cost - Actual cost| / |Actual cost|) x 100

The cubic function best represents the cost of tuition because out of the three models, the cubic regression has the least percent error to the actual cost of Franciscan's tuition. When calculating the percent error from the actual cost in 2014, the linear regression had about 10% error, a difference of about 7% from the cubic function, which was only about 3% off. The exponential regression was also off by about 8.5%, which is still a greater difference than that of the cubic function. For these reasons, the cubic regression best represents the tuition costs for Franciscan University.

Contrary to my expectations, the cubic model was better consistently than the other two models. When plugging in x=1, 5, and 10 for each of the equations, the cubic function was the closest to the actual cost of tuition during the years of 2001, 2005 and 2010. I expected the exponential function to be the most accurate, but it makes sense that the tuition cost is represented in a cubic function that reflects the economy's status.

In 1987, Franciscan's earliest enrollment year, the tuition cost was $5,220. When this value is added, the equations change as follow:

a. Linear - f(x)=630.077x+14929.979

b. Cubic - f(x)=1.491x^3-15.762x^2+400.177x+16359.382

c. Exponential - f(x)=13454.873 (1.058)^x

# Part C – Presentation and Reflection

This project has help us understand more clearly that college is not cheap, and that tuition will continue to rise every year. This will make us become mindful of the decisions we make when we apply for colleges. We have to take into account about what our families are able to afford and what scholarships you should apply for. We believe that we worked pretty hard and diligent on this project. In 40 weeks, we will be in our senior year, and will be applying to colleges. We will remember researching our favorite colleges and know the tuition growth very well. In 40 months, we will probably be in college and we will remember that kids in high school will be paying tuition higher than what we had to. In 40 years, we will probably still be trying to pay off our loans from college, and will remember that we knew coming into college that it would be expensive.