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Warm-Up: January 28, 2013 Write each as an integer or decimal

Warm-Up: January 28, 2013 Write each as an integer or decimal. 8% 2.4% 0.01% 3 6 (3 4 )(4 3 ) 24(2 3 ). Exponential Growth and Decay. Section 6.1. Essential Questions. What is exponential growth? What is exponential decay?. Exponential Growth.

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Warm-Up: January 28, 2013 Write each as an integer or decimal

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  1. Warm-Up: January 28, 2013Write each as an integer or decimal • 8% • 2.4% • 0.01% • 36 • (34)(43) • 24(23)

  2. Exponential Growth and Decay Section 6.1

  3. Essential Questions • What is exponential growth? • What is exponential decay?

  4. Exponential Growth • Exponential growth can be used to model a number of real-world situations, including population growth or bacteria growth.

  5. Bacteria (don’t need to copy) • Bacteria are very small, single-celled organisms that live almost everywhere on Earth. • Some are harmful to humans, but most are not. Some are helpful. • Bacteria reproduce by dividing into two. They do so at a constant rate, allowing us to create mathematical models of their population growth.

  6. Example 1 • A population of 100 bacteria doubles every hour. Predict the population after n hours

  7. Exponential Expression • Exponential Expression: An expression with a variable as an exponent and a fixed number as the base. • Base (Multiplier): In the exponential expression bx, b is the base, also called the multiplier. • 100(2n) is an exponential expression with a multiplier of 2

  8. Exponential Decay • A decay rate can be thought of as a negative growth rate. • The basic form is the same, but the multiplier is less than one.

  9. General Formula • If multiplier is greater than one, it is exponential growth. • If multiplier is between zero and one, it is exponential decay. • The multiplier must be written as a decimal, not a percent.

  10. Examples: Page 358, #16, 18Find the multiplier • 16) 9% growth • 18) 2% decay

  11. You-Try: page 358, #20, 22 • 20) 8.2% decay • 22) 0.08% growth

  12. Example: Page 359 #36Predict the population • Start with 55 bacteria that double every hour • a) after 3 hours • b) after 5 hours

  13. You-Try: Page 359 #40 • 225 bacteria that triple every hour • a) after 1 hour • b) after 3 hours

  14. Assignment • Pages 358-359 #15-24, 26, 30, 36-41

  15. Warm-Up: January 29, 2013 • A particular boulder in a river is being eroded at a rate of 2% per year. If the boulder’s mass is 250 kg today, what will it be in 30 years? • Hint: This is exponential decay.

  16. Homework Questions?

  17. Worksheet • You have the remainder of class to work on the 6.1 worksheets. • Due Thursday

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