From: Andrew Lorimer <andrew@lorimer.id.au>
Date: Mon, 25 Mar 2019 11:08:24 +0000 (+1100)
Subject: Merge branch 'master' of ssh://charles/tank/andrew/school/notes
X-Git-Tag: yr12~185
X-Git-Url: https://git.lorimer.id.au/notes.git/diff_plain/2e3b4eae42f5477f127dfdba183701b5d808665a?hp=79c757d262f3680e96db74a6d07ac7402d8aae0b

Merge branch 'master' of ssh://charles/tank/andrew/school/notes
---

diff --git a/methods/graphics/exponential-graphs.png b/methods/graphics/exponential-graphs.png
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diff --git a/methods/graphics/log-graphs.png b/methods/graphics/log-graphs.png
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diff --git a/methods/stuff.md b/methods/stuff.md
index cd3aeb0..2055b63 100644
--- a/methods/stuff.md
+++ b/methods/stuff.md
@@ -1,5 +1,5 @@
 ---
-geometry: margin=2cm
+geometry: margin=1.5cm
 <!-- columns: 2 -->
 graphics: yes
 tables: yes
@@ -41,7 +41,6 @@ If $a<1, \quad \log_{b} a < 0$ (flip inequality operator)
 
 $e^x$ - natural exponential function
 
-
 $$\lim_{h \rightarrow 0} {{e^h-1} \over h}=1$$
 
 ## Logarithm laws
@@ -65,10 +64,6 @@ $$f^{-1}: \mathbb{R}^+ \rightarrow \mathbb{R}, f^{-1}=log_ax$$
 
 $$e= \lim_{n \rightarrow \infty} (1 + {1 \over n})^n$$
 
-## Literal equations
-
-_Literal equation_ - no numerical solutions
-
 ## Exponential and logarithmic modelling
 
 $$A = A_0 e^{kt}$$
@@ -91,9 +86,11 @@ $$f(x)=Aa^{k(x-b)} + c, \quad \vert \> a > 1$$
 - dilation of factor $A$ from $x$-axis
 - dilation of factor $1 \over k$ from $y$-axis
 
+![](graphics/exponential-graphs.png){#id .class width=30%} 
+
 ## Graphing logarithmic functions
 
-$log_e x$ is the inverse of $e^x$ (reflection across $y=x$)
+$\log_e x$ is the inverse of $e^x$ (reflection across $y=x$)
 
 $$f(x)=A \log_a k(x-b) + c$$
 
@@ -106,6 +103,8 @@ where
 - dilation of factor $A$ from $x$-axis
 - dilation of factor $1 \over k$ from $y$-axis
 
+![](graphics/log-graphs.png){#id .class width=30%} 
+
 ## Finding equations
 
 Solve simultaneous equations on CAS: ![](graphics/cas-simultaneous.png){#id .class width=75px}
diff --git a/methods/stuff.pdf b/methods/stuff.pdf
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