Exponential Parameters: the 'b' Value

1. Fundamental Concepts
Definition: Exponential functions have the form

Growth vs. Decay:
If , the function shows exponential growth.
If , the function shows exponential decay.
Graph Description:
Growth ( ): the curve rises sharply to the right.
Decay ( ): the curve falls toward zero as increases.

2. Key Ideas
The larger the value of , the faster the growth.
The smaller the value of , the faster the decay.
The base directly determines the function’s shape.

3. Examples
Example 1 (Growth):

Example 2 (Decay):

4. Calculation Practice
Problem 1: Suppose . If , find .

Problem 2: Suppose . If , find .