Polynomial Equations versus Exponential Equations
You may be familiar with equations that contain exponents. Take the polynomial equation y = 2x^{2} + 5x – 7 for example. We see variables, and we see exponents. However, this is not an exponential equation. An exponential equation contains a variable exponent. This means that our variable x, for example, is part of the expression for the exponent, not a base number.
Generally, we say that an exponential equation is given by:
Exponential equation: an equation involving a constant value raised to a variable power.
We have a base number, b, being raised to a variable exponent, x. We also have an a-value in front, which is a scalar multiplier to the exponential expression.
Restrictions to the Base
The domain (or values that x is allowed to take on) is all real numbers, from negative infinity to positive infinity. As such, there are some restrictions to the base. These are values for b that come into direct conflict with the all real number domain:
Exponential Relationships in Tables
Let's look at a table of values for the exponential equation y = 3 • 2^{x}
When filling out values in a table, we apply the exponent first, and then multiply by the outside factor, as shown below:
In exponential equations, the exponent is applied to the base number first, and then multiplied by the scalar value in front of the exponential expression.
an equation involving a constant value raised to a variable power