From 0ab522b6571b42442998679a74b580b065135053 Mon Sep 17 00:00:00 2001 From: Andrew Lorimer Date: Sat, 23 Mar 2019 16:49:59 +1100 Subject: [PATCH 1/1] [methods] finalise exponential/log notes --- methods/graphics/exponential-graphs.png | Bin 0 -> 50457 bytes methods/graphics/log-graphs.png | Bin 0 -> 63492 bytes methods/stuff.md | 13 ++++++------- methods/stuff.pdf | Bin 45304 -> 231364 bytes 4 files changed, 6 insertions(+), 7 deletions(-) create mode 100644 methods/graphics/exponential-graphs.png create mode 100644 methods/graphics/log-graphs.png diff --git a/methods/graphics/exponential-graphs.png b/methods/graphics/exponential-graphs.png new file mode 100644 index 0000000000000000000000000000000000000000..ff049363064a9361f0f8538eb45deda3b35aa9b4 GIT binary patch literal 50457 zcmeFZbySpJ+crGt4-pVh0TB?8E(u9#L_q=RZs~66Q~{->rMtTu1f)BM?huBMZsyxF z-1qa{&-1Q#z2AS|KkvAfz%|3Z_I2iQ9_P97mz92pg+YV?fk3dt-@lcIKv0PxkUO95 z-vL)hX7$&>mw$|3OTC6bN<%TPbWy?2&-LHSOFhkgbmp 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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 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