One-Term Models
A One-Term Model describle the quantity changes over time using a single mathmatical term or expression. These models follow differential equation of the form:
where is the variable, represents time, and is the rate of change.
High-Order Polynomial Models
In some cases, models with more than one term will be considered, especially when a data set has asymptote(s). Thus, High-Order Polynomial models will be considered.
If there are data points, the highest order that can perfectly fit all the data points is .
Advantages and Disadvantages of High-Order Polynomials
High-Order Polynomials can approximate all data points, making future integral and derivative analyses more convenient.
On the other hand, consider a situation where data points form a positively sloped straight line, except for the last point, which is below the line. If a linear approximation is applied, the end of the line will continue to increase. However, if the high-order polynomial, such as quadrartic function, is used, the trend at the end may be decreasing.