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Exponential Functions

Section 5.1 focuses on evaluating exponential functions, finding specific values, graphing techniques, and application problems like doubling time and compound interest. Learn to find values, graph functions, and solve practical scenarios with exponential growth and decay. Explore examples in continuous compounded interest, population growth, and radioactive decay.

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Exponential Functions

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  1. Exponential Functions Section 5.1

  2. Evaluate the exponential functions Find F(-1) Find H(-2) Find Find F(0) – H(1)

  3. Natural Base = e • e is an irrational number • e is the base used in continuous compounded interest problems • Exponential Function • Find f(3)

  4. Steps to Graph Exponential Function • Find y intercept f(0) • Find 2 additional points above and 2 below intercept • Horizontal asymptote (x axis unless shifted) • As x increases • If b>1 then f(x) increases • If 0 < b < 1 then f(x) decreases

  5. Graph

  6. Graph

  7. Graph

  8. Graph

  9. Graph

  10. Graph

  11. Graph

  12. Graph

  13. Homework

  14. Day 2 Section 5.1 • Doubling Time Growth Model = Population at initial time (time = 0) P= Population at time t d = doubling time t = time

  15. Doubling time example • The current population of the island of Doon is 500,000 and it is expected to double in 15 years. Estimate the population in 5 years. = 500,000 d = 15, t = 5

  16. Half- life • Half-life Model = initial amount (time = 0) A= Amount at time t h = half-life in years t = time

  17. Half- life example • A radioactive isotope has a half-life of 119.77 days. If 200 milligrams are given to a patient, how many milligrams are left after 30 days?

  18. Compound Interest P= Principal r= rate n= number of times it is compounded in a year t= number of yers A= amount after t years

  19. Example of compound interest • If $10,000 is deposited in an account paying 4.5% compounding weekly, how much will you have in the account in 3.5 years?

  20. Continuous Compound Interest • P= principal • r= rate • t= number of years • A= amount after t years

  21. Example Compounded Continuously • If 10,000 is deposited in an account paying 4.5% compounded continuously, how much will you have in the account in 3.5 years?

  22. Homework • Page 435 50, 54, 58 - 64

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