# What are Exponential Equations? Give a concrete example of one.

## Question:

What are Exponential Equations? Give a concrete example of one.

## Exponential Equations:

There are a variety of equations that are used to model a plethora of phenomena, in problems of kinematics and ballistics, to those of growth rate and compounding interest. Functions, such like ones that are used to model bacterial growth rate or compounding interest for instance, are known as exponential equations.

Exponential equations are of the general form {eq}Y=ab^x {/eq}.

These types of equations may be used to model phenomena, which behave exponentially, such like bacterial growth. If we start with a single bacterium and monitor its growth through fission, where growth rate is taken with respect to growth per hour, we can ergo model growth rate via an exponential function, such like {eq}Y=a^x {/eq}, where {eq}x {/eq} is the number of hours.

Suppose that a bacterial colony triples in an hour, so the colony's growth can be represented by the exponential function {eq}Y=3^x {/eq}.