Exponential Function

Exponential functions:

• Continous
• One-to-one
• Domain = (-∞, ∞)
• Range = (0, ∞)
• Increasing if a > 1
• Decreasing if 0 < a < 1

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

Definition of Euler’s Number:

The Natural Base Exponential Function:

Growth if a > 0 AND r > 0
Decay if a > 0 AND r < 0

Compound Interest:

Doubling Time and Half-Life:
It is the time it takes for the function values to double OR for it to halve.

How to find a and b from two points:

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