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Warm up

Warm up. A rabbit population starts with 3 rabbits and doubles every month. What is the number of rabbits after 6 months?. Solution. After 6 months: 192 rabbits. Exponential Functions. Have you ever seen an exponential?.

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Warm up

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  1. Warm up A rabbit population starts with 3 rabbits and doubles every month. What is the number of rabbits after 6 months?

  2. Solution • After 6 months: 192 rabbits

  3. Exponential Functions

  4. Have you ever seen an exponential? • Have you noticed if you leave food out it might look fine for a few days, then get a little mold, then suddenly be extremely moldy? OR • Have you notices it takes hot coacoa a long time to cool enough to drink, but then it gets cold fast? • These are examples of exponential growth and decay.

  5. Definition of a exponential function • An exponential function is a function with the variable in the exponent. • It is used to model growth and decay. • The general form is

  6. Look at warm up to determine what the variables mean Let’s determine how many rabbits there are in the first 3 months. Month 0 is the starting amount. As we can see: a= starting number b= rate of change x= number of time intervals that have passed.

  7. Example 1 • How would we write this with exponents? Ask yourself 2 questions: 1. What is being repeated? 2. How many times is it repeated? Answers: 3 is being repeated 5 times. This equals

  8. Example 2 -You try! • Rewrite each expression with exponents 2.

  9. Answers 2.

  10. Example 3 • A house was purchased for $120,000 and is expected to increase in value at a rate of 6% per year. • Write an exponential function modeling the situation. • What is the value of the house after 3 years?

  11. Example 3: Solution • A house was purchased for $120,000 and is expected to increase in value at a rate of 6% per year. • Starting value is 120,000=a • Rate of increase is 1.06=b • Increases per year, so x will represent years.

  12. Solution cont… • How do we find the value after 3 years? • We know x represents years, so plug in 3 for x. • y= 142921.92

  13. Looking at the “b” in another way: Decay: if b is less than 1 Growth: If b is greater than 1

  14. Example 4- You try! • A population of 10,000 bugs increases by 3% every month. • How many bugs will there be after 5 months?

  15. Solution • A population of 10,000 bugs increases by 3% every month. • How many bugs will there be after 5 months? • a=10,000 • b= 1+.03 = 1.03 • x=5 • y= 11592 bugs

  16. Example 5 • Sarah buys a new car for $18,000. The car depreciates at a rate of 7% per year. How much will the car be worth after 5 years?

  17. Solution • Sarah buys a new car for $18,000. The car depreciates at a rate of 7% per year. How much will the car be worth after 5 years? • a=18,000 • b= 1-.07 = .93 • x=4 • y= 12,522.39

  18. Homework 6.2 Worksheet • Problems: • 1 • 2 • 3 • 6

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