1. Exponential and Logarithmic Functions
Chapter 8
Exponential and Logarithmic Functions

2. Please take out your iPad
Using Desmos, graph the following equation:
Y = 2x
Discuss with your neighbor the shape and direction of this graph.
Without erasing previous graphs, add the graphs of
Y = 5x
Y = .5x
Make a list of similarities and differences.

3. 8-1Exponential Models

5. 8-1Exponential Models

6. Write an exponential function for the graph which goes through (0,2) and (1, 1.3)

7. 8-1Exponential Models

8. 8-1Exponential Models

9. 8-1Exponential Models

10. 8-1Exponential Models

11. An exponential function takes the form
Y = abx
the “a” represents the initial or beginning value
The “b” represents the growth or decay rate
If the function is increasing b = 1 + r
If the function is decreasing b = 1 – r
Where r is the rate of change as a decimal
DO NOT multiply a and b together!

12. 8-1Exponential Models

14. 8-2 Properties of Exponential Functions

15. 8-2 Properties of Exponential Functions
Principal: $5000, interest rate 6.9%, 30 years
Principal: 20,000, interest rate 3.75%, 2 years

16. 8-2 Properties of Exponential Functions

17. 8-3 Logarithmic Functions
What exponent would you have to use to:
change 2 to 8?
change 7 to 1?
change 5 to 25?
change 3 to 81?
change 4 to 0.25?
When you are determining the exponent you would need to change a number to something else, you are finding the logarithm. Logarithms are exponents.

18. 8-3 Logarithmic Functions

19. 8-3 Logarithmic Functions

20. 8-3 Logarithmic Functions

21. 8-3 Logarithmic Functions

23. 8-3 Logarithmic Functions
Evaluate each logarithm

24. 8-3 Logarithmic Functions

25. 8-3 Logarithmic Functions
Sometimes you will need to convert each number to a power of the same base.

26. 8-4 Properties of Logarithms

27. 8-4 Properties of Logarithms

29. 8-4 Properties of Logarithms

34. 8-5 Exponential and Logarithmic Equations

35. 8-5 Exponential and Logarithmic Equations

36. 8-5 Exponential and Logarithmic Equations

37. Change of Base Formula

38. Logarithmic Equations

42. Change of Base Formula

46. warm up

47. 8-6 Natural Logarithms

53. 8-2 Properties of Exponential Functions

56. An initial population of 450 quail increases at an annual rate of 9%
An initial population of 450 quail increases at an annual rate of 9%. Write an exponential function to model the quail population.
The half life of a certain radioactive material is 60 days. The initial amount of the material is 785 grams. Write an exponential function to model the decay of this material.
Write the exponential function that contains the points (0,6) and (1,12)