1. Warm-Up: January 7, 2015
Determine whether each table below represents a linear function.

2. Homework Questions?

3. Functions, Graphs, and Tables
Investigation 5C
Advanced Integrated Math I

4. You-Trys
Determine whether each table below represents a linear function.

5. You-Trys
Determine whether each table below represents a linear function.

6. You-Try (with partner)
Use the tables above to make predictions. Will there be enough grain to feed the world in 2020? In 2030?
What kind of factors could change your predictions?

7. Assignment
Page 429 #11-13

8. Page 429

10. Warm-Up: January 8, 2015
Describe how to find each output using the previous output.

11. Homework Questions?

12. Section 5.13 Advanced Integrated Math I
Constant Differences
Section 5.13
Advanced Integrated Math I

13. Example
Copy and complete the table
Input
Output Δ 5 1 12 2 19 3 26 4 33 40

14. Definitions
Consecutive outputs are the outputs for consecutive inputs.
The differences between consecutive outputs are recorded in the Δ column.
If these differences are the same, that value is called the constant difference or common difference.
This also means the function is linear.

15. You-Try
Copy and complete the table
Input
Output Δ 4 3 1 2 -4 7 5

16. You-Try (with partner)
In the table, variables a and b represent arbitrary numbers.
Copy and complete the table in terms of a and b.
Find a linear function that matches the table.
Input
Output Δ b a 1 2 3 4 5

17. Assignment
Read Section 5.13 (pages )
Page 437 #6, 7, 8, 10, 12

18. Section 5.14 Advanced Integrated Math I
Recursive Rules
Section 5.14
Advanced Integrated Math I

19. Recursive Rules
Recursive rules tell how to get from one output to the next output.
An initial output, called the base case, must also be given.

20. Fibonacci Sequence Base Case: Recursive Rule:
What are the first 10 numbers in the Fibonacci Sequence?

21. You-Try
Describe a recursive formula that agrees with the table.
Input
Output 3 1 7 2 11 15 4 19 5 23

22. You-Try (with partner)
Does the recursive rule
define the function ?
Test your answer with an input of ½

23. You-Try (with partner)
James saves $85 and wants to invest it.
Investment L will add $5 at the end of every year to James’s account.
Investment E will add 5% of the current amount at the end of every year.
Which investment is better in the short run?
Which investment is better in the long run?

24. Assignment
Read Section 5.14 (pages )
Page 445 #8-11, 13, 14

26. Warm-Up: January 12, 2015
You may use a calculator (graphing or otherwise) to complete this warm-up.

27. Input, x
Output, y 1 2 3 4 5

28. Homework Questions?

29. Investigation 5A Quiz Questions?

30. Section 5.15 Advanced Integrated Math I
Constant Ratios
Section 5.15
Advanced Integrated Math I

31. Definitions An exponential function is one where x is in the exponent.
The ratio of outputs is one output divided by the previous output.
Exponential functions have a constant ratio.

32. Explicit  Recursive

33. Assignment
Read Section 5.15 (page )
Page 452 #5, 6, 8, 11

34. Page 452
See textbook for #5, 6, 11

36. Warm-Up: January 13, 2015
Tony invests $600 in a savings account that earns 3% interest at the end of each year.
How much interest will he have earned after 1 year?
How much interest will he have earned after 2 years?

37. Homework Questions?

38. Section 5.16 Advanced Integrated Math I
Compound Interest
Section 5.16
Advanced Integrated Math I

39. You-Try (with partner)
Tony finds a new investment for his $600 that earns 6% interest at the end of each year.
How much interest will he earn after 2 years?
Is it double the amount he would earn with the 3% investment?

40. Interest
Most bank accounts calculate interest based on the current balance and add the amount to the account.
When the interest on the current balance includes interest on previous interest, it is called compound interest.
Compound interest is usually calculated and added to the account more often than once per year.

41. Example 1
Tony finds another investment that offers 5.9% interest compounded monthly. Why is this the best option so far?

42. Interest Formula A = current amount
P = principal (the original investment)
r = Interest rate (APR), expressed as a decimal, not as a percent
n = Number of times per year interest is calculated
t = Time, measured in years

43. Example 2
Tony decides to invest his money in a CD (certificate of deposit) that earns 6% APR, compounded annually. How many years will it take for his investment to double?

44. Assignment Read Section 5.16 (pages 456-459)

45. Page 460 #5, 6, 10, 11, 12

47. Warm-Up: January 14, 2015 On Monday we looked at functions of the form
For what values of b will the outputs be increasing (for increasing inputs)?
For what values of b will the outputs be decreasing (for increasing inputs)?

48. Homework Questions?

49. Graphs of Exponential Functions
Section 5.17
Advanced Integrated Math I

50. Exponential Growth and Decay
Exponential growth occurs when a>0 and b>1.
Exponential decay occurs when a>0 and 0<b<1.

51. Real World Applications
Exponential Growth
Exponential Decay
Population growth
People
Bacteria
Continuous compounding of interest
Nuclear reactions
Processing power of computers (Moore’s Law)
Half-lives of radioactive isotopes
Carbon dating
Other dating to determine ages of dinosaurs, etc.
Rate of cooling (temp.)
First order chemical reaction rates
Atmospheric pressure (as a function of height)

52. Assignments Read Section 5.17 (pages 462-464) Page 465 #5-8
Graphs must be on graph paper
Page 467 #1-5

53. Page 465
See textbook for #7