1 / 23

Chapter 3: Exponential and Logarithmic Functions

Chapter 3: Exponential and Logarithmic Functions . Bellwork. Name the following types of functions: 1.Y=(4x+2)/(2-x²) 2.Y=x²-4x+10 3.Y=5cos (3x) + 7 4.Y=9ˣ-8 5.Y=5x – 2 ***Quadratic, trigonometric, linear, exponential, or rational***.

noam
Télécharger la présentation

Chapter 3: Exponential and Logarithmic Functions

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. Chapter 3: Exponential and Logarithmic Functions

  2. Bellwork • Name the following types of functions: 1.Y=(4x+2)/(2-x²) 2.Y=x²-4x+10 3.Y=5cos (3x) + 7 4.Y=9ˣ-8 5.Y=5x – 2 ***Quadratic, trigonometric, linear, exponential, or rational***

  3. Exploration: Exponential FunctionsCLE 3126.3.4 Identify or analyze the distinguishing properties of exponential functions from tables, graphs, and equations. F(x)= aˣ • Let a = 1 The graph is _____________ • Let a<0 What happens when x is even? Odd? • Let a > 1 What does the graph look like? What do you notice about the table? • Let 0<a<1 What does the graph look like? What do you notice about the table?

  4. Exponential Growth and Decay

  5. Explore Further • F(x)=3ˣ • Describe the graph. Include any special point(s) on the graph. • Compare G(x) = 15ˣ and H(x) = 2ˣ to the above graph. • Discuss domain and range of each.

  6. Let’s Move • Given: f(x)=2ˣ • Change the equation so that the new graph will reflect f(x) about the y-axis. • How does this relate to our knowledge of the graph when 0<a<1? • Change the equation so that the graph shifts up 3. Compare the graphs and tables. • Change the equation so that the graph shifts left 5. Compare the graphs and tables.

  7. CLE 3126.3.4 Identify or analyze the distinguishing properties of exponential functions from tables, graphs, and equations. • F(x) = C(aˣ) • F(x)=3ˣ What is the value of C? • Where is the value of c graphically? • Change C to explore its purpose. Compare graphically and numerically(table) • Positive values • Negative values

  8. Journal • Given: F(x)=C(aˣˉ ͪ)+k Explain how a, C, h, and k work together to create different exponential graphs.

  9. Practice • Sketch f(x)=3(2ˣˉ²)+1 • Check with partner and calculator. • CLE 3126.3.4 Identify or analyze the distinguishing properties of exponential functions from tables, graphs, and equations.

  10. 3126.3.16 Solve real world problems that can be modeled using quadratic, exponential, or logarithmic functions (by hand and with appropriate technology). • Formula for compound interest: • bi-annually – interest every two years (n = .5) – quite rare • annually – interest once a year (n = 1) – somewhat rare • semi-annually - interest twice a year (n = 2) – somewhat rare • quarterly – interest every 3 months (n = 4) – somewhat common • monthly - interest every month (n = 12) – some banks do it • weekly – interest every week (n = 52) – quite rare • daily – interest every day (n = 365) – most banks do it

  11. Compound Interest • Jack invested $5000 in a long term Certificate of Deposit 50 years ago. The CD earns 4.5% interest compounded monthly. How much is in the CD today? • How much more money would Jack have earned if the CD had compounded daily?

  12. Compound Continuously Using the (1+r/n)^n part of the compound interest formula, let r=1(100%). Put the expression into y1. Look at the table. For larger and larger values of n to what value does the expression tend?

  13. The natural number: e • Compound continuously: A=Pe ͬ ͭ • Twenty-two years ago, I bought a CD that has been earning 4.2% interest compounding continuously. If it is now worth $7, 350, how much was it worth when I bought it?

  14. Match the Exponential Graph • http://www.teachmaths-inthinking.co.uk/exponential-graphs/exponential-games.htm

  15. Half Life • The half-life of Carbon-14 is 5730 years. If a human being whose body contains 1.64 x 10^-8 grams of Carbon-14 died today, how much Carbon-14 would be left in 8595 years?

  16. Half Life • I lost 4 grams of Strontium-90 in my garage. Strontium-90 has a half-life of 28.8 years. Write a formula for the function f(x) that expresses how much Strontium-90 is left after t years have gone by. • How much Strontium-90 will be left when my house is bulldozed to make way for some gaudy monstrosity in 70 years?

  17. Doubling Time • The approximate number of fruit flies in an experimental population after t hours is given by Q(t)=20e^(.03t) • What is the initial population of fruit flies? • What is the doubling time for the fruit fly population? • How large is the population of fruit flies after 72 hours?

  18. Journal • Explain in half life and doubling time in your own words.

  19. Bellwork • Without a calculator approximate the following values of x. • 5=2^x • 11=8^x • 45=5^x

  20. 3.2 Logarithmic Functions and Their Graphs CLE 3126.3.4 Identify or analyze the distinguishing properties of logarithmic functions from tables, graphs, and equations. Exponential Form: y=a^x Logarithmic Form: Restrictions on a?

  21. Compare Numerically and Graphically • Y= 2 ͯ • Y=log₂x • Sketch F(x)=log₆x without the calculator Compare the two logarithms on the calculator. What changes should be made to the equation to shift F(x) to the right?left? What changes should be made to F(x) to shift the equation up? Down?

  22. Properties of Logarithms • logₐ1= • logₐa= • logₐa ͯ= • a^logₐx= • If logₐx=logₐy, then x=

  23. CLE 3126.3.4 Identify or analyze the distinguishing properties of logarithmic functions from tables, graphs, and equations. • What is the inverse of y=e ͯ?

More Related