1 / 11

3.1 Exponential Functions and their Graphs

3.1 Exponential Functions and their Graphs. Students will recognize and evaluate exponential functions with base a. Students will graph exponential functions. Students will recognize, evaluate, and graph exponential functions with base e.

ross
Download Presentation

3.1 Exponential Functions and their Graphs

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. 3.1 Exponential Functions and their Graphs Students will recognize and evaluate exponential functions with base a. Students will graph exponential functions. Students will recognize, evaluate, and graph exponential functions with base e. Students will use exponential functions to model and solve real-life problems.

  2. Example 1 Use a calculator to evaluate each function at the indicated value of x. a. b. c.

  3. y 2 x –2 Example 2 In the same coordinate plane, sketch the graph of each function by hand. • b.

  4. y 2 x –2 Example 3 In the same coordinate plane, sketch the graph of each function by hand. • b.

  5. y 2 x –2 Example 4 Each of the following graphs is a transformation of • b. c. d.

  6. Compound Interest Annually Compounded Interest: = Accumulated amount after n years P = principle (invested amount) r = the interest rate in decimal form (5% = .05) n = time in years Compounded Interest m times per year: m = # of times per year interest is compounded (i.e. m = 1 is yearly, m = 12 is monthly, m = 365 is daily) Compounded Interest continuously: e is the natural number

  7. Example: Invest $1 for 1 year at 100% Consider how m affects the accumulated amount: Yearly m = 1 Bi-annually m = 2 Monthly m = 12 Daily m = 365 Hourly m = 8760 Example 5

  8. Continuously CompoundedInterest:

  9. y 2 x –2 Example 6 Use a calculator to evaluate the function where: • b. c.

  10. Example 7 A total of $12000 is invested at 7% interest. Find the balance after 10 years if the interest is compounded a) quarterly b) continuously a) b)

More Related