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Do Now

Do Now. Clickulators . If , then evaluate . 60. The length of the larger base of a trapezoid is 10 cm. It has a height of 5 cm and an area of . What is the length of the small base in square centimeters?. 60. Given that , what will be the last digit of .

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Do Now

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  1. Do Now • Clickulators.

  2. If , then evaluate 60

  3. The length of the larger base of a trapezoid is 10 cm. It has a height of 5 cm and an area of . What is the length of the small base in square centimeters? 60

  4. Given that , what will be the last digit of . • Cannot be determined from given information 60

  5. Given is an invertible function and solve for : . 60

  6. Frankie took four tests and got an average score of 87.5%. If his fifth test raised his average to 90%, what was his score on that test? 60

  7. Given that quadrilateral is a square and is equilateral. If determine the distance between and rounded to the nearest meter. 60

  8. Objectives CRS • NCP 703: Exhibit knowledge of logarithms and geometric sequences 13.November.2012 • Students will be able to… • Evaluate, analyze, and graph exponential functions • Solve problems involving exponential growth and decay.

  9. Exponential Functions • Let and • How are and different? • Functions similar in form to are exponential functions

  10. Exponential Functions • Which ones are exponential functions?

  11. Graphs of exponential functions • For the parent function: . • Domain: • All real numbers • Range:

  12. Growth Versus Decay • Exponential Growth • Exponential Decay

  13. Transformations

  14. Most real world applications of involving exponential growth or decay don’t involve base 2 or 10, but actually an irrational number named • It is derived using calculus to determine the value of the function as .

  15. Applications • Compound interest: • A bank account has interest. If Brufus invests $1000, how much will he have after 1 one year if the bank compounds: • Annually? • Monthly? • Daily? • Quarterly?

  16. Annually: • Monthly • Daily

  17. Compounded Continuously • Let , • Find: • This is what most banks use to calculate interest.

  18. Compound Interest • If $1000 is invested in a savings account earning 8% interest per year and compounded continuously, how much will be in the account at the end of 10 years if there are no other deposits or withdrawals?

  19. Growth and Decay • Annual growth/decay: • If is growth rate, is positive. • If it is a decay rate, is negative • Continuous growth/decay • If is growth rate, is positive. • If it is a decay rate, is negative

  20. Applications • Mexico has a population of approximately 110 million. If Mexico’s population grows at the rate of 1.42% annually, predict its population in 10 and 20 years.

  21. Applications • Mexico has a population of approximately 110 million. If Mexico’s population grows at the rate of 1.42% continuously, predict its population in 10 and 20 years.

  22. Applications • In 1980, there were 190.9 cases of chicken pox. In 2005, there were 32.2 cases of chicken pox. If the rate of chicken pox cases is decreasing exponentially, determine the rate of decrease.

  23. Doubling • If you invest in a savings account offering 3.5% interest compounded continuously, how long until your money doubles?

  24. Practice • Pg. 166 #25 • Pg. 167 #35

  25. Exit Ticket • Pg. 166 #31 • Pg. 167 #36

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