Exponential Functions

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

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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