I have a problem in which I am given following data

Year Number of Students

1980 3401

1983 7462

1986 4492

1989 4288

1992 6493

1995 7538

1998 12699

I am being asked to calculate when the enrollment was increasing and decreasing, also to find the maximum and the minimum of the curve. I do not have any problems doing all of that as long as I have a polynomial function, but that is where my problem lies... I do not know how to determine the equation of the polynomial that best models the given data.

On the question it says "Using graphing technology, determine the equation of the polynomial that best models the given data. However, I do not have access to any scientific calculator that can do that for me.

Any help with this would be appreciated. I just need to know the principle behind determining polynomial equations from table data.

Thank you!