AP Precalculus / Unit 2: Exponential and Logarithmic Functions
2.3 Exponential Functions
Notes
$f(x)=ab^x$ with $a\ne0$, $b>0$, $b\ne1$.
- $b>1$: growth. $0<b<1$: decay.
- The horizontal asymptote of $ab^x$ is $y=0$.
- $f(0)=a$ is the initial value.
Practice
$f(x)=4(0.5)^x$ is:
$0<b<1$.
The $y$-intercept of $f(x)=3\cdot2^x$:
$3\cdot2^0$.
As $x\to\infty$, $5(0.8)^x\to$
Decay approaches the asymptote $y=0$.
Ready for more? Take the Unit 2 test.