Lecture 4.1 bt

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Lecture 4.1 bt

  1. 1. Today’s Agenda  Attendance  Sections 4.1 / Announcements
  2. 2. Payday! You just got a job! You will work for 30 days. You may choose between three pay rates. Rate Plan A pays $200,000 a day. Rate Plan B pays $50,000 your first day and provides you with a $10,000 raise each subsequent day. (For instance, you earn $60,000 on the second day, $70,000 the third day, and so forth.) Rate Plan C pays 2 cents the first day and doubles every subsequent day. (For instance, you earn 4 cents on the second day, 8 cents on the third day, and so forth)
  3. 3. Payday! Rate Plan A pays $200,000 a day.
  4. 4. Payday! Rate Plan B pays $50,000 your first day and provides you with a $10,000 raise each subsequent day. (For instance, you earn $60,000 on the second day, $70,000 the third day, and so forth.)
  5. 5. Payday! Rate Plan C pays 2 cents the first day and doubles every subsequent day. (For instance, you earn 4 cents on the second day, 8 cents on the third day, and so forth)
  6. 6. Payday! Rate Plan C pays 2 cents the first day and doubles every subsequent day. (For instance, you earn 4 cents on the second day, 8 cents on the third day, and so forth)
  7. 7. Payday! Rate Plan C pays 2 cents the first day and doubles every subsequent day. (For instance, you earn 4 cents on the second day, 8 cents on the third day, and so forth)
  8. 8. Exponential Functions Variable is in exponent f ( x) b x base *Just because a function has an exponent, doesn’t mean it is an exponential function
  9. 9. f ( x) 3x 2 4x 2x 1 g ( x) 3 h( x) 3 x 3 h(t ) 3x 2 f ( x) 3 2 x2 1 1
  10. 10. Basic Graphs f ( x) 2 x
  11. 11. Basic Graphs f ( x) 2 x
  12. 12. Basic Graphs f ( x) 1 2 x
  13. 13. Basic Graphs f ( x) 2 x 3
  14. 14. Basic Graphs f ( x) 2 x 3
  15. 15. This is considered Exponential Growth
  16. 16. What common point do they all pass through?
  17. 17. This is considered Exponential Decay
  18. 18. Exponential Functions with Initial Values Some unit of time (usually) f ( x) Initial Value, or initial population a b x Rate of growth or decay
  19. 19. Exponential Functions with Initial Values Some unit of time (usually) P (t ) Initial Value, or initial population P0 r t Rate of growth or decay
  20. 20. …Quick Algebra Check!... 3 2 1 2 4 2 3
  21. 21. A bacteria starts with an initial count of 3000 and doubles every hour. How many bacteria after 3.5 hours? When will there be 25,000 bacteria?
  22. 22. A bacteria starts with an initial count of 3000. An antibiotic is introduced, causing half of the bacteria to die off each hour. How many bacteria after 3.5 hours? When will there be 500 bacteria?
  23. 23. Classwork • Page 220 1 – 6 All 19, 20 – 30 all, 45, 49

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