[chem] reaction rate prac results

diff --git a/methods/stuff.md b/methods/stuff.md
index adbb286512fed3d4a61ce11188ba44829a41645e..fb94066fe41f81f2354aa5c6747d75205814d015 100644 (file)
--- a/methods/stuff.md
+++ b/methods/stuff.md
@@ -50,6 +50,7 @@ $\log_a(m^p) = p\log_am$
 $\log_a(m^{-1}) = -\log_am$  
 $\log_a1 = 0$ and $\log_aa = 1$
 
+
 ## Inverse functions
 
 Inverse of $f: \mathbb{R} \rightarrow \mathbb{R}, f(x)=a^x$ is $f^{-1}: \mathbb{R}^+ \rightarrow \mathbb{R}, f^{-1}=log_ax$
@@ -57,3 +58,31 @@ Inverse of $f: \mathbb{R} \rightarrow \mathbb{R}, f(x)=a^x$ is $f^{-1}: \mathbb{
 ## 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
+
+