Do Now

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

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