Colloquially the term exponential is generally used for functions where the relevant domain includes an "elbow" and where the local maximum is at least orders o

Colloquially the term exponential is generally used for functions where the relevant domain includes an "elbow" and where the local maximum is at least orders of magnitude larger than the local minimum. Or put another way -- any exponential function can be locally approximated by a linear function, so we might use the term exponential growth for a function where growth is poorly approximated by a linear function over the relevant domain