Exponential Function

Exponential functions:

y 
ax, orf(x) ax, 
One-to •one 
Domain: ( 
Range: (O, m ) 
Increasingifa > I 
Decreasing if O < a < I 
Horizontal asymptote is x-axis 
Pintercept: (O, I)

One-to-One Functions:
If different inputs have different outputs, and vice versa AKA one x-value doesn’t have multiple y-values

Horizontal-Line Test:
If a horizontal line touches the function more than once, then it is NOT a One-to-One Function

Doubling Time and Half-Life:

Exponential Growth Model 
Doubling Time 
In 2 
kT — In 2, or k — 
In 2 
or T 
k

How to write an exponential function, with two points given:

OR

Yl

And then substitute the a, x and y-values in and solve for b

Things to remember:
Always Round-UP when dealing with years
Ex. 2005.2 is 2006 obviously

Exponential equations that are a little tricky:

ㄨ | 0 一 e¯ 
5 e 
10 
一 乀 0 = 0 
j00 · 一

Find the rate or time in a compound interest equation: