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UNIT 5: Exponential Growth / Decay Formula:

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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 Expression
1. 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 Inequalities
b) 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)


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