Exponential Growth Decay Formula a original amount yintercept

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… • 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>0 a y<0 • Y-intercept= a

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

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

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:

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

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

Example 4 a) Solving Exponential Equations / Inequalities b)

Example 5 a) Applications 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.

Example 5 b) Applications 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)