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

4. 8-1Exponential Models

5. 8-1Exponential Models

6. 8-1Exponential Models

7. 8-1Exponential Models

8. 8-1Exponential Models

9. 8-1Exponential Models

11. 8-2 Properties of Exponential Functions

12. 8-2 Properties of Exponential Functions

13. 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.

14. 8-3 Logarithmic Functions

15. 8-3 Logarithmic Functions

16. 8-3 Logarithmic Functions

17. 8-3 Logarithmic Functions

19. 8-3 Logarithmic Functions
Evaluate each logarithm

20. 8-3 Logarithmic Functions

21. 8-3 Logarithmic Functions
Sometimes you will need to convert each number to a power of the same base.

22. 8-4 Properties of Logarithms

23. 8-4 Properties of Logarithms

25. 8-4 Properties of Logarithms

30. 8-5 Exponential and Logarithmic Equations

31. 8-5 Exponential and Logarithmic Equations

32. 8-5 Exponential and Logarithmic Equations

33. Change of Base Formula

34. Change of Base Formula

35. Logarithmic Equations

42. warm up

43. 8-6 Natural Logarithms

51. 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)