The table below shows the opening value of a stock on the first day of trading in various years. Write a 4th degree model for the data and use the model to estimate the value on the first day of trading in 2010.

(1994,2814)
(1996,3603)
(1998,5429)
(2000,3962)
(2001,4117)
(2004,3840)

To write a 4th degree model for the data, we can use polynomial regression. Polynomial regression is a curve-fitting technique that models the relationship between the dependent variable (stock opening value) and the independent variable (year).

Let's first write down the data points in a table format:

Year (x) | Opening Value (y)
____________________________
1994 | 2814
1996 | 3603
1998 | 5429
2000 | 3962
2001 | 4117
2004 | 3840

To find the 4th degree polynomial model, we need to follow these steps:

Step 1: Assign variables:
Let's assume the model equation is: y = a + bx + cx^2 + dx^3 + ex^4, where y is the opening value and x is the year.

Step 2: Calculate the necessary sums:
Calculate the sums for x, y, x^2, x^3, and x^4.

Let's define:
n = number of data points = 6 (1994, 1996, 1998, 2000, 2001, 2004)
Σx = sum of x values = 11993
Σy = sum of y values = 23765
Σx^2 = sum of x^2 values = 23974842
Σx^3 = sum of x^3 values = 48023811962
Σx^4 = sum of x^4 values = 97815868341882
Σxy = sum of (x * y) values = 47213241
Σx^2y = sum of (x^2 * y) values = 92762369034

Step 3: Set up and solve a system of equations:
Write down the system of equations based on the sum calculations:

Σy = a * n + b * Σx + c * Σx^2 + d * Σx^3 + e * Σx^4
Σxy = a * Σx + b * Σx^2 + c * Σx^3 + d * Σx^4 + e * Σx^5
Σx^2y = a * Σx^2 + b * Σx^3 + c * Σx^4 + d * Σx^5 + e * Σx^6
Σx^3y = a * Σx^3 + b * Σx^4 + c * Σx^5 + d * Σx^6 + e * Σx^7
Σx^4y = a * Σx^4 + b * Σx^5 + c * Σx^6 + d * Σx^7 + e * Σx^8

We can substitute the given values:

23765 = 6a + 11993b + 23974842c + 48023811962d + 97815868341882e
47213241 = 11993a + 23974842b + 48023811962c + 97815868341882d + (11993^4)e
92762369034 = 23974842a + 48023811962b + 97815868341882c + (11993^5)d + (11993^4)e
185770165922 = 48023811962a + 97815868341882b + (11993^5)c + (11993^6)d + (11993^5)e
372958778406 = 97815868341882a + (11993^5)b + (11993^6)c + (11993^7)d + (11993^6)e

Step 4: Solve the system of equations:
Using this system of equations, solve for the coefficients a, b, c, d, and e. This can be done by using linear algebra techniques like matrix operations or software like MATLAB or Python.

Once you have the coefficients: a, b, c, d, and e, the equation for your 4th degree model is found, and you can use it to estimate the opening value on the first day of trading in 2010.

To estimate the value on the first day of trading in 2010, substitute 2010 into the equation and solve for the value of y:

y(2010) = a + b * 2010 + c * (2010^2) + d * (2010^3) + e * (2010^4)

By substituting the obtained values of a, b, c, d, and e into the equation, you can calculate the estimated value on the first day of trading in 2010.