# College Cost Project

## Linear, Cubic & Exponential Models - Texas State

linear: y= 986.909x + 5795.273

cubic: y=-11.729x^3 + 207.065x^2 + 4.692x + 6684.503

exponential: y= 6404.173 x 1.099^x

## Linear, Cubic & Exponential Models - BYU

linear: y=320.909x + 5493.636

cubic: y= -1.068x^3 + 33.671x^2 + 83.341x + 5796.783

exponential: y=5612.441 x 1.045^x

## Texas State

Predictions

1990-91

linear: y= 986.909(-10)+5795.273= \$-4,073.82

cubic: y= -11.729(-10)^3+207.065(-10)^2+4.692(-10)+6684.503= \$39,073.08

exponential: y= 6404.173 X 1.099^(-10)= \$2,491.64

2014-15

linear: y= 986.909(14)+5795.273= \$19,612.00

cubic: y= -11.729(14)^3+207.065(14)^2+4.692(14)+6684.503= \$15,150.56

exponential: y= 6404.173 X 1.099^(14)= \$24,012.13

2018-19

linear: y= 986.909(18)+5795.273= \$23,559.64

cubic: y= -11.729(18)^3+207.065(18)^2+4.692(18)+6684.503= \$5,454.49

exponential: y= 6404.173 X 1.099^(18)= \$35,028.50

2040-41

linear: y= 986.909(40)+5795.273= \$45,271.63

cubic: y= -11.729(40)^3+207.065(40)^2+4.692(40)+6684.503= \$-412,479.82

exponential: y= 6404.173 X 1.099^(40)= \$279,492.88

Actual Tuition

1990-91: \$2,382

2014-15: \$16,660

Percent Error

1990-91:

Linear: 271.03%

Cubic: 1540.36%

Exponential: 46.03%

2014-15:

Linear: 17.72%

Cubic: 9.06%

Exponential: 44.13%

## BYU

Predictions

1990-91

linear: y=320.909(-10)+5493.636= \$2,284.55

cubic: y= -1.068(-10)^3+33.671(-10)^2+83.341(-10)+5796.783= \$9,398.47

exponential: y=5612.441 X 1.045^(-10)= \$3,614.01

2014-15

linear: y=320.909(14)+5493.636= \$9,986.36

cubic: y= -1.068(14)^3+33.671(14)^2+83.341(14)+5796.783= \$10,632.48

exponential: y=5612.441 X 1.045^(14)= \$10,393.93

2018-19

linear: y=320.909(18)+5493.636= \$11,297.00

cubic: y= -1.068(18)^3+33.671(18)^2+83.341(18)+5796.783= \$11,977.75

exponential: y=5612.441 X 1.045^(18)= \$12,394.96

2040-41

linear: y=320.909(40)+5493.636= \$18,330.00

cubic: y= -1.068(40)^3+33.671(40)^2+83.341(40)+5796.783= \$-5347.98

exponential: y=5612.441 X 1.045^(40)= \$32,644.00

Actual Tuition

1990-91: \$1,800

2014-2015: \$10,000

Percent Error

1990-91:

Linear: 26.92%

Cubic: 422.14%

Exponential: 100.77%

2014-2015:

Linear: -.13%

Cubic: 6.32%

Exponential: 3.94%

## #6

The exponential function best models the cost of tuition for both schools. The cubic model was the farthest from being the best. The values predicted by using the exponential model for the 1990-1991 and 2014-2015 tuition are overall closest to the actual researched tuition during those years compared overall to the other models. For example, this year in 2014-2015 at BYU, the yearly tuition rate was \$10,000 and the exponential equation produced the value \$10,393.93 which is reasonably close. For Texas state, in 1990-1991, the yearly tuition was \$2,382. The exponential model produced the value \$2,491.64 which is also reasonably close to the actual tuition. Although the exponential model did not perfectly match the actual tuition values for the school in 1990-91 and 2014-2015, they were overall the most realistic to the trend of the costs over time.

## #7

No, not one model was more consistent than the other. None of them consistently gave solutions that were mostly accurate to the actual tuition prices. This is not what we expected because we thought that the exponential model would be most consistent because the function best fit the cost of tuition for each school, however it was not consistent. All three functions would one time be very close to the actual tuition price with a small percent error and then the next year, it would have an extremely large percent error. Overall this was not what we expected, especially because we expected for one model to be more consistent than the others.

## #8

Texas State

Linear: 216.801x+9785.833

Cubic: 0.272x^3+25.47x^2+707.142x+6227.668

Exponential: 7774.036 x 1.056^x

Linear:

Tuition 1990-91:\$-1054.22

Tuition 2014-2015: \$12, 821.05

Cubic:

Tuition 1990-91:\$545.57

Tuition 2014-15: \$21,866.14

Exponential:

Tuition 1990-91: \$4508.24

Tuition 2014-15: \$17,253.10

BYU

Linear: 130.782x+6478.841

Cubic: .253x^3+13.681x^2+160.669x+5746.493

Exponential: 5305.999 x 1.057^x

Linear:

Tuition 1990-91: \$-60.25

Tuition 2014-15: \$8309.79

Cubic:

Tuition 1990-91: \$327.01

Tuition 2014-15:\$11,370.88

Exponential:

Tuition 1990-91: \$3038.97

Tuition 2014-15: \$11,577.77

By adding the new value at 1964, the cubic regression model seems to become the more precise equation to use. The exponential regression model's tuition from 1990-91 became much higher and less exact. The linear regression model is not the right choice either because it would allow you negative money, which is not possible.

## Reflection

This project has influenced our college searches because it has helped us know what to expect with changing tuitions. Using the models we can estimate how much the tuition will be raised (or lowered) while attending the schools we researched, which greatly helps make financial decisions when choosing colleges. We very much enjoyed this project and the real world application we experienced through it. We worked very hard and collaborated well on this project. In 40 weeks we will remember the changes in tuition when we are applying and being accepted into college. In 40 years when we are sending our own children off to college, we can look back at there graphs and see how accurate their estimates are.