For continuous growth, $k > 0$
For continuous decay, $k < 0$
-## Graphing expomnential functions
+## Graphing exponential functions
$$f(x)=Aa^{k(x-b)} + c, \quad \vert \> a > 1$$
-- **$y$-intercept** at $(0, A \cdot a^{-kb}+c)$
+- **$y$-intercept** at $(0, A \cdot a^{-kb}+c)$ as $x \rightarrow \infty$
- **horizontal asymptote** at $y=c$
- **domain** is $\mathbb{R}$
- **range** is $(c, \infty)$
where
- **domain** is $(b, \infty)$
-- **range** is $\mathbb{R}^+$
+- **range** is $\mathbb{R}$
- **vertical asymptote** at $x=b$
- $y$-intercept exists if $b<0$
- dilation of factor $A$ from $x$-axis