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 \(0<b<1\).


Go to Explore (Graphs of Growth and Decay)