2. 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?

3. Applications that Apply to Me!

4. Exponential Functions Always involves the equation: b x Example: 2 3 = 2 · 2 · 2 = 8

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

6. The Table: Results XF(x) = 2 x 2 -1 = ½ 02 0 = 1 12 1 = 2 22 2 = 4 32 3 = 8

7. The Graph of y = 2 x

8. 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?

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

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

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

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

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

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

15. 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

16. 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

17. Exponential Decay: Car Depreciation Depreciation Rate Value after 2 years Value after 5 years Value after 8 years Value after 10 years 10% $16,200$11,809.80$8609.34$6973.57 Assume the car was purchased for $20,000 Formula: y = a (1 – r) t a = initial amount r = percent decrease t = number of years

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