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Exponential Functions: Writing, Applying, and Solving

This lesson focuses on writing and applying exponential functions, including choosing the appropriate form of equation for a given context and using the equation to answer questions. Homework includes practicing these skills with various exercises.

jonathanmoore
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Exponential Functions: Writing, Applying, and Solving

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  1. Simplify. Warm Up

  2. Ch 5- day 2 Writing and applying exponential functions Leave the class being able to: 1: choose the appropriate form of equation for the given context 2. Write an equation from context 3. Use your equation to answer questions.

  3. Homework: To: P173 #1-31 every third, or 33-43 odd ADD 5.2, p178: 33-43 odd, 5.2 Exponential Functions

  4. Classwork part 1 • IN your textbook: do class exercises 1, 2, 5-9all, 13, 17, On page 177

  5. 5.3 Exponential Functions Domain: Range:

  6. Find a function given the initial value + plus one additional value

  7. Find an exponential function with the given values: 1. 2.

  8. Different forms of Exponential Equationsform number 1 of 5 Time Y = a(b)x Growth or Decay Factor Starting amount

  9. Different forms of Exponential equationform 2 of 5 • Exponential growth and decay- given a rate: • Use , where r is the rate, as a decimal. r is positive for growth, negative for decay

  10. Exponential equation form #3, of 5 • Exponential growth and decay- given an outcome and the time to achieve it: • Use: • Where b is the outcome, in other words, “what happened”- for examples: reduced by ½, doubled, multiplied by 4 • And k is how long it takes to do that.

  11. Different forms of Exponential Functions 1. 2. 3. 5.3 Exponential Functions

  12. Different forms of Exponential Functions 1. 2. 3. 5.3 Exponential Functions Convert the 2nd form to the 1st form.

  13. $1000 Suppose you invest some money that grows to the amount, , in t years. • How much did you invest? • How long does it take to double your money? 10 years Suppose that t hours from now the population of a bacteria colony is given by • What is the population when t = 0? • What will the population be in 8 hours? 90 100 times larger = 9000

  14. 5.3 Exponential Functions Convert the 2nd form to the 1st form.

  15. 5.3 Exponential Functions

  16. 5.3 Exponential Functions How long will it take for a savings account of $1000 to grow to $2000 if it earns a 9% annual rate of interest?

  17. 5.3 practice • Class exercises: • P182 1-10 all

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