1. 1. Warm-Up 4/21 D

3. Rigor: You will learn how to evaluate, analyze, graph and solve exponential functions. Relevance: You will be able to solve population problems and solve half-life chemistry problems using exponential functions.

4. 3-1 Exponential Functions

5. Algebraic Functions are functions are solved using algebraic operations. Transcendental Functions are functions that can not be expressed in terms of algebraic operations. They transcend Algebra. Exponential and Logarithmic Functions are transcendental functions.

6. Example 1a: Sketch and analyze the graph of the function. Describe its domain, range, intercepts, asymptotes, end behavior, and where the function is increasing, or decreasing. xy – 30.04 – 20.11 – 10.33 01 13 29 327 Domain: Range: y -intercept: Asymptotes: End Behavior: Increasing/Decreasing: and

7. Example 1b: Sketch and analyze the graph of the function. Describe its domain, range, intercepts, asymptotes, end behavior, and where the function is increasing, or decreasing. xy – 38 – 24 – 12 01 1.5 2.25 3.125 Domain: Range: y -intercept: Asymptotes: End Behavior: Increasing/Decreasing: and

9. xy – 4.125 – 3.25 – 2.5 – 11 02 14 28 xy – 3.125 – 2.25 – 1.5 01 12 24 38

10. xy – 38 – 24 – 12 01 1.5 2.25 3.125 xy – 3.125 – 2.25 – 1.5 01 12 24 38

11. xy – 3–.375 – 2–.75 – 1– 1.5 0– 3 1– 6 2– 12 3– 24 xy – 3.125 – 2.25 – 1.5 01 12 24 38

12. xy – 36.1x10 –6 – 23.4x10 –4 – 1.01832 01 154.598 22981 3162755 xy – 4.01832 – 3.04979 – 2.13534 – 1.36788 01 12.7183 27.3891 320.086 454.598

13. xy – 323.086 – 210.389 – 15.7183 04 13.3679 23.1353 33.0498 xy – 3.04979 – 2.13534 – 1.36788 01 12.7183 27.3891 320.086

14. xy – 3.02489 – 2.06767 – 1.18394 0.5 11.3591 23.6945 310.043 xy – 3.04979 – 2.13534 – 1.36788 01 12.7183 27.3891 320.086

16. Example 4: Krysti invest $300 in an account with 6% interest rate, making no other deposits or withdrawals. what will Krysti’s account balance be after 20 years if the interest is compounded: a.semiannually? b.Monthly? c.Daily? P = 300, r = 0.06, t = 20 n = 2 n = 12 n = 365

17. Example 5: Suppose Krysti invest $300 in an account with 6% interest rate, making no other deposits or withdrawals. What will Krysti’s account balance be after 20 years if the interest is compounded continuously? P = 300, r = 0.06, t = 20

18. a.1.42% annually b.1.42% continuously Example 6: Mexico has a population of approximately 110 million. If Mexico’s population continues to grow at the described rate, predict the population of Mexico in 10 and 20 years. N 0 = 110,000,000 r = 0.0142,t = 10 and t = 20 k = 0.0142

19. math! 3-1 Assignment: TX p166, 4-32 EOE Test Corrections Due Friday 4/25 Chapter 3 test Thursday 5/1