1 / 11

Lesson 3.1 Exponential Functions and their Graphs

Lesson 3.1 Exponential Functions and their Graphs. Example 1. y = 10 x. y = 3 x. Example 2. y = 2 -x. y = 10 -x. Exponential Functions a → “the base ”; positive & b → y-intercept (when x = 0) Graphs of Exponentials: ► f(x ) > 0 ( y-values are always positive)

india-walton
Download Presentation

Lesson 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. Lesson 3.1Exponential Functionsand their Graphs

  2. Example 1 y = 10x y = 3x

  3. Example 2 y = 2-x y = 10-x

  4. Exponential Functions a → “the base”; positive & b→ y-intercept (when x = 0) Graphs of Exponentials: ► f(x) > 0 (y-values are always positive) ► Must pass through (0, 1) ► Patterns: Parent Function

  5. Example 3 For both functions, graph them by hand, identify any asymptotes and intercepts, tell whether they are increasing or decreasing, and state how they are related through transformations. g

  6. Example 4: Half Life • The mass of radium-226 with a half-life of 1590 years is given by the equation: • What is the initial mass? • How much of the element is left after 1000 years? • When will one quarter of the element be remaining?

  7. Compound Interest A = amount of interest (growth) P = principal (starting amount) r = % interest (growth) – yearly n = periods per year t = time (years) Example 5Find the amount in interest on $3000 invested at 8% compounded quarterly for 5 years.

  8. Just for fun…find: $1 @ 10% yearly = $1 @ 10% quarterly = $1 @ 10% monthly = $1 @ 10% daily = $1 @ 20% daily = $1 @ 50% daily = $1 @ 90% daily = $1 @ 100% daily =

  9. The Number e $1.00 earning 100% a year compounded continuously will yield $2.72 For the next 50 quarters you receive, the chance of getting all 50 state quarters is You get to pick one song from a group of 100 to download. Once you listen to the next song you may not go back. To get your favorite song you should pick the 37th song. This is the next song after

  10. e: an important math number like π, Φ Find: e1 = e2 = e3 = e is a popular base in math when there is continous growth → growth: A = Pert → decay: A = Pe-rt

  11. Example 6 Estimates are given for the population growth of two cities: and Before graphing, determine a reasonable viewing window. Graph both functions. Will ever pass ? If so, when?

More Related