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Merge branch 'patch-14' into 'master'

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Cleaning up a little bit, otherwise it's very good

See merge request magicalsoup/Highschool!39
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James Su 2020-02-20 00:06:07 +00:00
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Grade 10/Math/MCR3U7/Unit 1: Exponential and Logarithmic Functions.md
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@ -2,7 +2,7 @@
## Review ## 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 $`(\dfrac{1}{k}x+d, ay+c)`$. 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 $`y`$. To solve/find the inverse of a function, just swap the $`y`$ and $`x`$ and isolate/solve for $`y`$.
## Exponential Decay/Growth ## 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. 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
- $`R = 1 + r`$ - $`R = 1 + r`$
- **half-life:** $`R = \dfrac{1}{2}`$ - **half-life:** $`R = \dfrac{1}{2}`$
- **doubling time:** $`R = 2`$ - **doubling time:** $`R = 2`$
**Growth Rate** **Growth Rate**
- $`r > 0`$ Exponential Growth - $`r > 0`$: Exponential growth
- $`-1 \lt r \lt 0`$ Exponential Decay - $`-1 \lt r \lt 0`$: Exponential decay
- r is ually given as a $`\%`$ - 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