$\log_a(m^{-1}) = -\log_am$
$\log_a1 = 0$ and $\log_aa = 1$
+
## Inverse functions
Inverse of $f: \mathbb{R} \rightarrow \mathbb{R}, f(x)=a^x$ is $f^{-1}: \mathbb{R}^+ \rightarrow \mathbb{R}, f^{-1}=log_ax$
+
+## Euler's number
+
+$$e= \lim_{n \rightarrow \infty} (1 + {1 \over n})^n$$
+
+## Literal equations
+
+_Literal equation_ - no numerical solutions
+
+## Exponential and logarithmic modelling
+
+$$A = A_0 e^{kt}$$
+
+where
+$A_0$ is initial value
+$t$ is time taken
+$k$ is a constant
+For continuous growth, $k > 0$
+For continuous decay, $k < 0$
+m
+## Graphing expomnential functions
+
+$$f(x)=Aa^{k(x-b)} + c, \quad \vert a > 1$$
+
+- **$y$-intercept** at $(0, {{1+c} \over {a^b}})$
+- **horizontal asymptote** at $y=c$
+- **domain** is $\mathbb{R}$
+- **range** is $(c, \infty)$
+- dilation of factor $A$ from $x$-axis
+- dilation of factor $1 \over k$ from $y$-axis
+
+