#5 Exponential Functions
What is an Exponential Function? By definition, it’s a function that grows or decays at a constant rate.
Graphs of Exponential Functions
Exponential vs. Linear
When it comes to exponential and linear functions, understanding the difference between the two can save you a lot of headache, especially when it comes to word problems.
| Exponential | Linear |
|---|---|
| Common form; ab^x | Common form; mx+b |
| a=y-intb=multiplier | m=slopeb=y-int |
| Change in Y; multiply by b | Change in Y; +/- m |
| “Tip off” language;- “decreased/increased by _ PERCENT”- “DOUBLED every hour” | “Tip off” language;- “increases at a CONSTANT RATE”- “decreased by __ PER year” |
Translating Repeating Percent Increases/Decreases
Like I said before, percentages are a tip off that let you know you’re dealing with an exponential function, but how do you add it to the equation?
- When given a percentage the equations you use are; 1+p/100 or 100+p/100, whatever is easier to remember
- Plug it into the equation like this; y=a(1+p/100)^x