**Exponential functions
**

An *exponential function* is a functions whose explicit function expression has the form *y* = *C B*^{x}. *C* and *B* are constants, and the input variable *x* is in the exponent.

Exponential functions can be defined recursively by

NEW = OLD + (*k*)OLD, with some START value.

This definition is equivalent to

NEW = (1 + *k*)OLD, with that START value.

The number 1 + *k* becomes *B* of the explicit function expression, and the START value becomes *C*.

The number (*k*)OLD is the rate of change of the exponential function
defined this way. The rate of change is proportional to the value of the
function (OLD).

The constant *k* is sometimes called the *relative growth rate,* and 1 + *k* is called the *growth factor.*

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