1. UNIT 5: 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 about…
b cannot be negative b > 1 growth 0 < b < 1 decay
DOMAIN of all exponential functions is: all real numbers (no restrictions for x)
RANGE of exponential functions: + a  y > 0 - a  y <0
Y – INTERCEPT = a

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

4. Graph each of the following. Find domain and range. 1.2. 4. 3.

5. Simplifying Exponential Expressions
LAWS OF EXPONENTS
Remember when you multiply terms with same base, ADD exponents
When you raise a power to a power, MULTIPLY exponents

6. Practice: Simplify each Expression1. 2. 4. 3.

7. Solving Exponential Equations / Inequalities
Example 3:
Solving Exponential Equations / Inequalities
Basic Steps: 1] FACTOR into common bases
2] CANCEL common bases
3] SOLVE equation / inequality c) a) b)

8. Example 4 Solving Exponential Inequalitiesb) a) b)

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)