FNGR 1 | Lesson 2 | Explore (Equation of an Exponential Function)

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 \(0<b<1\).

Go to Explore (Graphs of Growth and Decay)