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

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

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)

Graph each of the following. Find domain and range. 1. 2. 4. 3.

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

Practice: Simplify each Expression 1. 2. 4. 3.

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)

Example 4 Solving Exponential Inequalities b) a) b)

Example 5 Applications a) A bacteria colony is growing exponentially each day. There was initially had 100 bacteria and after 3 days it had 800. Write an equation to represent this growth, and tell how many bacteria after 10 days.

(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 2000. Write an equation to represent the growth, and predict the population in 2010. (0, 10,000) (6, 29,860)