1 / 18

Understanding Exponential Growth & Decay in Real Life Scenarios

Explore exponential functions with practical examples like investment growth, money doubling, and car depreciation. Learn the equations, formulas, and calculations to predict value changes over time. Enhance your math skills for real-world applications.

carr
Download Presentation

Understanding Exponential Growth & Decay in Real Life Scenarios

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. Do Now • Three years ago you bought a Lebron James card for $45. It has appreciated (gone up in value) by 20% each year since then. How much is worth today?

  2. Exponential Growth & Decay Applications that Apply to Me!

  3. Exponential Functions • Always involves the equation: bx • Example: • 23 = 2 · 2 · 2 = 8

  4. Group investigation:Y = 2x • Create an x,y table. • Use x values of -1, 0, 1, 2, 3, • Graph the table • What do you observe.

  5. The Table: Results

  6. The Graph of y = 2x

  7. Observations • What did you notice? • What is the pattern? • What would happen if x= -2 • What would happen if x = 5 • What real-life applications are there?

  8. Group: Money Doubling? • You have a $100.00 • Your money doubles each year. • How much do you have in 3 years? • Show work.

  9. Money Doubling Year 1: $100 · 2 = $200 Year 2: $200 · 2 = $400 Year 3: $400 · 2 = $800

  10. Earning Interest on • You have $100.00. • Each year you earn 10% interest. • How much $ do you have in 3 years? • Show Work.

  11. Earning 10% results Year 1: $100 + 100·(.10) = $110 Year 2: $110 + 110·(.10) = $121 Year 3: $121 + 121·(.10) = $133.10

  12. Exponential Growth Model The Formula is: y = a(1+r)t a = Initial Amount r = Growth Rate (1+r) = Growth Factor t = Time Period

  13. Using the Equation • $100.00 • 10% interest • 5 years • 100(1+ (.10))5 = $161.05 • What could we figure out now?

  14. Exponential Decay Model Instead of increasing, it is decreasing. Formula: y = a(1–r)t a = Initial Amount r = Decay Rate (1-r) = Decay Factor t = Time Period

  15. Real-life Examples • What is car depreciation? • Car Value = $20,000 • Depreciates 10% a year • Figure out the following values: • After 2 years • After 5 years • After 8 years • After 10 years

  16. Exponential Decay: Car Depreciation Assume the car was purchased for $20,000 Formula: y = a (1 – r)t a = initial amount r = percent decrease t = number of years

  17. Homework Textbook: • Page 481 #24-28 • Page 489 #26-30

More Related