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Exponential Growth / Decay Formula :

Exponential Decay. Exponential Growth. Exponential Growth / Decay Formula :. a = original amount (y-intercept). b = growth factor (1 ± r ). y = final amount. x = unit of measure (time, bounces, etc.). Things to know…. b cannot be negative b>1 growth , b<1 decay

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Exponential Growth / Decay Formula :

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

  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>0 - ay<0 • Y-intercept= a

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

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

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

  8. b) a) Example 4Solving Exponential Equations / Inequalities

  9. Example 5Applications 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.

  10. Example 5Applications 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)

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