# FNGR 1 | Lesson 2 | Explore (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 $$\Large \frac{1}{4}$$
-1 $$\Large \frac{1}{2}$$
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 $$0<b<1$$.