# Equation of an Exponential Function

The tables below are from the first lesson we reviewed on exponential functions and recalling their structure.

$$x$$ $$y=2x$$
$$-2$$  $$-4$$
$$-1$$  $$-2$$
0  0
1  2
2  4
$$x$$ $$y=2^x$$
$$-2$$ $$\dfrac{1}{4}$$
$$-1$$ $$\dfrac{1}{2}$$
0  1
1  2
2  4

Function $$b$$ is of the form $$f(x)=ab^x$$. Recall this is an exponential function, where $$a$$ is the initial value, $$f(0)=a$$.

Exponential growth occurs when a quantity increases by the same constant ratio in each given time period. This occurs when $$b>1$$.

Exponential decay occurs when a quantity decreases by the same constant ratio in each time period. This occurs when $$0<b<1$$.