1. Exponential Growth / Decay Formula:
a = original amount (y-intercept)
b = growth factor (1 ± r)
y = final amount
x = unit of measure (time, bounces, etc.)
Exponential Growth
Exponential Decay

2. Things to know… b cannot be negative b>1 growth, b<1 decay
Domain of all exponential functions is: all real numbers (no restrictions for x)
Range of exponential functions: + ay> ay<0
Y-intercept= a

3. Example 1 Graphing a) b)
Example 2 Identifying Growth & Decay a) b)
Growth (b >1)
Decay (0 < b <1)

4. Graphing Graph each of the following. Find domain and range. 1. 2. 3.4.

5. Simplifying Exponential Expressions
Remember when you multiply terms with same base, add exponents
Ex:
When you raise a power to a power, multiply exponents
Ex:

6. Practice
Simplify each expression 1. 2. 4. 3.

7. Example 3 Solving Exponential Equations / Inequalities
Basic Steps: 1] Factor into common bases
2] Cancel common bases
3] Solve equation / inequality a) b)

8. Example 4 Solving Exponential Equations / Inequalitiesb)

9. Example 5 Applications
a) A bacteria colony is growing exponentially each day.
There was initially had 100 bacteria and after 3 days
it had Write an equation to represent this growth,
and tell how many bacteria after 10 days.

10. (0, 10,000) (6, 29,860) Example 5 Applications
b) A towns population is growing exponentially. In 2000,
the population was 10,000. By 2006 it had risen to 29,860.
Let x = 0 represent Write an equation to represent
the growth, and predict the population in 2010.
(0, 10,000)
(6, 29,860)