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UNIT 5: Exponential Growth / Decay Formula :

Exponential Growth. Exponential Decay. 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.). Things to know about…. b cannot be negative b > 1 growth 0 < b < 1 decay

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UNIT 5: Exponential Growth / Decay Formula :

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  1. Exponential Growth Exponential Decay 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.)

  2. Things to know about… • b cannot be negative b > 1 growth0 < b < 1 decay • DOMAINof all exponential functions is: all real numbers (no restrictions for x) • RANGEof exponential functions: + a  y > 0 - a  y <0 • Y – INTERCEPT = a

  3. Example 2Identifying Growth & Decay a) b) Example 1Graphing a) b) c) d)

  4. 2. • Graph each of the following. Find domain and range. 1. 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. c) a) b) Example 3: Solving Exponential Equations / Inequalities Basic Steps: 1] FACTOR into common bases 2] CANCEL common bases 3] SOLVE equation / inequality

  8. Example 4Solving Exponential Inequalities c) b) a)

  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.

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