1 / 21

1.3

1.3. Exponential Functions. What you’ll learn about…. Exponential Growth Exponential Decay Applications The Number e …and why Exponential functions model many growth patterns. Rules for Exponents. Exponential Function. Exponential Growth. Exponential Growth.

alta
Download Presentation

1.3

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. 1.3 Exponential Functions

  2. What you’ll learn about… • Exponential Growth • Exponential Decay • Applications • The Number e …and why Exponential functions model many growth patterns.

  3. Rules for Exponents

  4. Exponential Function

  5. Exponential Growth

  6. Exponential Growth If 0 < a < 1, then the graph of f looks like the graph of y = 2-x = .5x.

  7. Compound Interest The formula for calculating the value of an investment that is awarded annual compound interest is T=P(1+r)twhere T is the total value of the investment, P is the principal, r is the rate of interest (as a decimal) and t is the number of years.

  8. Calculate the value of a 3 year certificate of deposit given the initial investment was $500 and the CD earns 2% annually.

  9. If an investment earns 4% annually, how long will it take for the value of the investment to double?

  10. Half-life Exponential functions can also model phenomena that produce decrease over time, such as happens with radioactive decay. The half-life of a radioactive substance is the amount of time it takes for half of the substance to change from its original radioactive state to a non-radioactive state by emitting energy in the form of radiation.

  11. Exponential Growth and Exponential Decay The function y = k ● ax, k > 0, is a model for exponential growth if a > 1, and a model for exponential decay if 0 < a < 1.

  12. Example Exponential Functions Use a graphing calculator to find the zero’s of f(x)= 4x – 3.

  13. The Number e

  14. The Number e The exponential functions y = exand y = e-x are frequently used to model exponential growth or decay. Interest compounded continuously uses the model y = P ert, where P is the initial investment, r is the interest rate (as a decimal) and t is the time in years.

  15. Example The Number e • The approximate number of fruit fies in an experimental population after t hours is given by Q(t) = 20e0.03t, t ≥ 0. • Determine the initial number of flies in the poplation. • How large is the population after 72 hours? • Graph the function. [0,100] by [0,120] in 10’s

  16. Quick Review

  17. Quick Review

  18. Quick Quiz Sections 1.1 – 1.3

  19. Quick Quiz Sections 1.1 – 1.3

  20. Quick Quiz Sections 1.1 – 1.3 3. The half-life of a certain radio active element is 8 hours. There are 5 grams present initially. Which of the following gives the best approximation when there will be 1 gram remaining? • 2 • 10 • 15 • 16 • 19

  21. Assignment pages 26 – 28, 3-21 multiples of 3, 23-27, 32, 36, 40

More Related