From 2b814b5a0b4744b2610dc8a85b4114617dd7c35f Mon Sep 17 00:00:00 2001 From: Daniel Chen Date: Wed, 19 Feb 2020 16:26:59 +0000 Subject: [PATCH] Cleaning up a little bit, otherwise it's very good --- ...: Exponential and Logarithmic Functions.md | 20 +++++++++---------- 1 file changed, 10 insertions(+), 10 deletions(-) diff --git a/Grade 10/Math/MCR3U7/Unit 1: Exponential and Logarithmic Functions.md b/Grade 10/Math/MCR3U7/Unit 1: Exponential and Logarithmic Functions.md index fc35413..f46cb64 100644 --- a/Grade 10/Math/MCR3U7/Unit 1: Exponential and Logarithmic Functions.md +++ b/Grade 10/Math/MCR3U7/Unit 1: Exponential and Logarithmic Functions.md @@ -2,7 +2,7 @@ ## Review -A function is a relation where each x-value maps to exactly one y-value. +`Function`: A relation where each x-value maps to exactly one y-value. If given a function in the form $`y = af[k(x-d)] + c`$, then let $`(x,y)`$ be the original points, the new points will be $`(\dfrac{1}{k}x+d, ay+c)`$. @@ -26,7 +26,7 @@ A vertical line test is used to test whether a relation is a function. If any 2 To solve/find the inverse of a function, just swap the $`y`$ and $`x`$ and isolate/solve for $`y`$. ## Exponential Decay/Growth -When the base ($`b`$) is in the range $`0 \lt b \lt 1`$, the exponential funciton is said to have a **exponential decay**, the smaller the base, the stronger the decay. +When the base ($`b`$) is in the range $`0 \lt b \lt 1`$, the exponential function is said to have a **exponential decay**, the smaller the base, the stronger the decay. When the base ($`b`$) is in the range $`b \gt 1`$, the exponential function is said to have a **exponential growth**, the bigger the base, the stronger the growth. @@ -78,20 +78,20 @@ N = N_0(R)^{\frac{t}{d}} ``` -$`N = `$ Final amount. +$`N = `$ Final amount -$`N_0 = `$ Starting amount. +$`N_0 = `$ Starting amount -$`R =`$ Growth factor. +$`R =`$ Growth factor - $`R = 1 + r`$ - **half-life:** $`R = \dfrac{1}{2}`$ - **doubling time:** $`R = 2`$ **Growth Rate** -- $`r > 0`$ Exponential Growth -- $`-1 \lt r \lt 0`$ Exponential Decay -- r is ually given as a $`\%`$ +- $`r > 0`$: Exponential growth +- $`-1 \lt r \lt 0`$: Exponential decay +- r is usually given as a percentage ($`\%`$) -$`t = `$ Total amount. (time for $`N_0`$ to get to $`N`$) +$`t = `$: Total time for $`N_0`$ to get to $`N`$ -$`d = `$ Growth Rate time. (Time for 1 Growth Rate to occur). +$`d = `$ Time for 1 growth rate to occur