1. Warm Up  Complete the Grok Activity on the back of your homework (the one with people at the top)

2. Exponential Functions October 15 th

3. Exponential Functions An exponential function is a function with a variable in the exponent. f(x) = a(b) x

4. Exponential Functions Parent graphs of exponential functions are in the form: f(x) = b x Parent function- original function before any changes have been made. for example: f(x) = 4 x

5. Let’s review … Original Function: f(x) = b x f(x) = -b x Negatives in front cause a reflection across the x- axis. (make the graph flip)

6. Original Function: f(x) = b x f(x) = b x-1 f(x) = b x+1 rightleft  Numbers in the exponents cause horizontal shifts (right, or left).

7. Original Function: y = b x f(x) = b x - 1 f(x) = b x + 1 downup  Numbers behind the original function cause vertical shifts (down, and up).

8. Original Function: f(x) = b x f(x) = a(b) x Numbers larger than 1 that are in front of the b value cause a stretch.

9. Identify the parent function of each, and the transformations: 1. f(x) = 3 x – 8 2. f(x) = -3(2) x 3. f(x) = 4 x+5 4. f(x) = 2 x + 2 5. f(x) = 5 x-2

10. f(x) = 3(2) x XY -2 0 1 2 3 Domain: Range: Parent Graph: Transformation:

11. Asymptotes  All exponential functions have horizontal asymptotes.  Notice that the range values of the previous graph were restricted by the horizontal asymptote.  Range is always restricted by the asymptotes.

12. f(x) = 4 x-3 XY -2 0 1 2 3 Domain: Range: Parent Graph: Transformation:

13. f(x) = -8(.5) x XY -2 0 1 2 3 Domain: Range: Parent Graph: Transformation:

14. Warm Up  Complete the two examples from the notes yesterday that we did not complete: 1. f(x) = 3 x + 2 2. f(x) = -2 x - 3

15. f(x) = 3 x + 2 XY -2 0 1 2 3 Domain: Range: Parent Graph: Transformation:

16. f(x) = -2 x - 3 XY -2 0 1 2 3 Domain: Range: Parent Graph: Transformation:

19. Growth and Decay and Interest October 16 th

20. Exponential Growth

21. Growth Graphs  Of the following, which graphs show exponential GROWTH?

22. Evaluating an Exponential Function

23. Example:

24. Exponential Decay

25. Growth Graphs  Of the following, which graphs show exponential DECAY?

26. Exponential Growth/Decay y = a(b) x Equation: A = P(1 ± r) t.  A represents the final amount.  P represents the initial amount.  r represents the rate of growth/decay expressed as a decimal.  t represents time.

27. Exponential Growth/Decay y = a(b) x Key words to look for that tell you to use the formula is increase, appreciate and growth. Key words to look for that tell you to use the formula is decrease, depreciate and decay.

28. Examples 1. The original price of a tractor was $45,000. The value of the tractor decreases at a steady rate of 12% per year. a. Write an equation to represent the value of the tractor since it was purchased. b. What is the value of the tractor in 5 years?

29. You Try 2. Find a value of a $20,000 car in five years if it depreciates at a rate of 12% annually. Write the exponential function to model the situation, and find the amount after the specified time.

30. Exponential Growth/Decay y = a(b) x Equation: A = P(1 ± r) t.  A represents the final amount.  P represents the initial amount.  r represents the rate of change expressed as a decimal  t represents time. Key words to look for that tell you to use the formula is increase, appreciate and growth. Key words to look for that tell you to use the formula is decrease, depreciate and decay.

31. Initial Amount you Borrow or Deposit Annual Rate of Interest (as a decimal) # of times the interest is compounded per year # of years the amount is deposited or borrowed for

32. What does n equal when you compound … ? 12 2 1 52 4

33. 3. The Lieberman’s have $12,000 in a savings account. The bank pays 3.5% interest on savings accounts, compounded monthly. Find the balance in 3 years.

34. 4. Determine the amount of an investment if $300 is invested, at an interest rate of 6.75%, compounded semiannually for 20 years.

35. Homework  Worksheet