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Mastering Exponential Growth & Decay: Formulas, Graphs, and Applications

Learn about exponential growth and decay in this comprehensive guide. Discover the formulas, graphing techniques, and practical applications. Practice simplifying expressions and solving equations. Master the laws of exponents and understand the behavior of exponential functions.

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Mastering Exponential Growth & Decay: Formulas, Graphs, and Applications

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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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