1. Warm Up Determine the better model for each data set
Find each function. Round to nearest tenth
Calculate f(-12), f(5), and f(21). Round nearest tenth 1 2

2. Warm Up Answers 1 2
Quadratic
Linear

3. Three Basic Function Models
Linear – Steady Increase or Decrease in Values
Quadratic – Decreases then Increases OR Increases then Decreases
Exponential – Increasing Increase or Decreasing Decrease in Values

4. Example of Exponential Function Model
Suppose the Centers for Disease Control (CDC) has determined that each day that a student with the flu comes to school, they infect two other people. Assume an infected person immediately becomes contagious.

5. Example of Exponential Function Model
Day 0: 1 Person is Infected
Day 1: 1+2 New = 3 Infected. (Total Increase: 2)
Day 2: 3+6 New = 9 Infected. (Total Increase: 6)
Day 3: New = 27 Infected. (Total Increase: 18)
Day 4: New = 81 Infected. (Total Increase: 54)

6. An Exponential Function can always be written in the following form:
In our example, 1 person was infected on Day 0, 3 people were infected by Day 1, 9 people were infected by Day 2, 27 people were infected by Day 3, etc.

7. This function will model our data perfectly if we set P=1, m=3 and let x represent the day number

8. If we want to estimate how many people will be infected after 10 days we simply let x=10
As you can see, exponential functions can get very large, quite quickly

9. Notice what happens to the value of f(x) when m is less than 1.

10. Exponential Functions are used quite often to model such natural occurrences as population growth and decline.

11. Example 1: Population Growth
In an experiment at the Centers for Disease Control, a specimen of e-coli bacteria is cultured. The population of the bacteria quadruples every hour. If the culture began with 10,000 bacteria, how many bacteria will there be after 24 hours?

12. Let f(x) represent the population of the bacteria and let x represent the number of hours the culture has been established.

13. Example 2: Population Decline
The bat population in the Northeast United States has been devastated by a phenomena called “white nose syndrome.” Every year, 40% of the bats in one particular cave die from this disease. If the current population of bats in the cave is approximately 2,500, how many living bats would scientists expect to find 5 years from now?

14. Let f(x) represent the population of the bats and let x represent the number of years from now.
Where did the number 0.6 come from?

15. Exponential Functions – Warm Up
The population of a particular beetle is given by the exponential function:
where x represents the year. Find the beetle population in 1990, 2000, 2009 and predict the population in 2015.

17. Finding Exponential Models
Enter your data tables as you did with Linear and Quadratic models, then
Press STAT Calc 0ExpReg Enter

18. 1. Find the Exponential Model for the Data Table Below

19. 1. Find the Exponential Model for the Data Table Below

20. 2. Find the Exponential Model for the Data Table Below

21. 2. Find the Exponential Model for the Data Table Below

22. 3. Find the Exponential Model for the Data Table Below
3. Find the Exponential Model for the Data Table Below. Round to the nearest thousandth

23. 3. Find the Exponential Model for the Data Table Below

24. 4. Find the Exponential Model for the Data Table Below
4. Find the Exponential Model for the Data Table Below. Round to the nearest thousandth

25. 4. Find the Exponential Model for the Data Table Below

28. Homework

30. Homework Answers Pg 452-453 #1-4, 9-20, 37-40
Rises, Falls
(0,1)
Does Not
243
(1,0) 2

31. Homework Answers Pg 452-453 #1-4, 9-20, 37-40

32. Homework Answers Pg 452-453 #1-4, 9-20, 37-40
37. a) 0.5°C b) .35°C
37. a) 1.0°C b) 0.4°C
39. a) 1.6°C b) 0.5°C
40. a) 3.0°C b) 0.7°C