Linear or exponential?
Definitions
A quantity grows (or decays):
- linearly, if it grows (decays) by a constant amount for each unit of time.
- exponentially, if it grows (decays) by a constant factor or rate for each unit of time.
Choosing a linear vs. an exponential model
When data are given in a table...
If you have a table of values, and the independent variable values (input values) are distant units from each other, you have two important indicators that allow you to guess which model best fits your data: the difference and the quotient of the corresponding outputs in the table.
If, for all inputs that are distant units from each other:
- the difference of the corresponding outputs is constant, then the data set in the table can be modeled by a linear function.
- the quotient of the corresponding outputs is constant, then the data set in the table can be modeled by an exponential function.