1. Day 2 : Exponent Rules and Growing Sequences
CCM1 Unit 5
Day 2 : Exponent Rules and Growing Sequences

2. Warm Up 2 – January 23th

3. Homework Check 5.1
Score = Dependent, Time = independent 4. M = 1 5. x < y 7. y=2x+5 8. x=

4. Essential Questions:
How can I apply properties of exponents to simplify expressions? When given a sequence, how do I identify its type and how do I write a rule for the sequence?

5. Exponent Rules Review
Exponents are a “short-hand” way of multiplying the same quantity over and over. Example: X4 = (x)(x)(x)(x)

6. Expand the following
1) 43 2) Y4 3) X2y5 4) w6z1

7. Using Exponents to simplify
Write using exponents
1) (x)(x)(x)(x)
2) (2)(2)(2)(2)(x)(x)(x)(y)(y)
3) (3)(3)(3)(4)(4)(4)(4)(x)

8. Zero as an exponent Anything with an exponent of zero equals 1.
Ex: x0 = 1
2) 60 =
3) Y0 =

9. Negative Exponents When you have a NEGATIVE exponent
Create a fraction if not one (make the denominator 1)
Move the base with the negative exponent to the other part of the fraction.
Make that exponent POSITIVE.
EX. x-3

10. Try Some
1) ) 3)

11. Ex: x4x2 Why can we just add the exponents? Ex:x4x2
Multiplication
When multiplying like bases you ADD exponents
Ex: x4x2
Why can we just add the exponents? Ex:x4x2
= [(x)(x)(x)(x)][(x)(x)] = x6

12. Simplify:
1) x3x4 2) y3x4y7 3) z3y2x5z5y6x10

13. Exponents of Exponents
When you have an exponent of an exponent you MULTIPLY
EX: (x4)3
Why can you multiply exponents?
(x4)3
= x4x4x4x4
= [(x)(x)(x)(x)][(x)(x)(x)(x)][(x)(x)(x)(x)] = x12

14. Try Some!
1) (x)5 2) (x2y4)5 3) (2x3)6

15. Division When you divide like bases you SUBTRACT exponents
Fix any negatives if they show up!!

16. Try Some
1) 2)
3) 4)

17. Growing Sequences
Arithmetic Sequence : goes from one term to the next by always adding (or subtracting) the same value
Common Difference : The number added (or subtracted) at each stage of an arithmetic sequence
Initial Term : Starting term
For example, find the common difference and the next term of the following sequence:
3, 11, 19, 27, 35, . . .

18. Growing Sequences
Geometric Sequence: goes from one term to the next by always multiplying (or dividing) by the same value
Common Ratio: The number multiplied (or divided) at each stage of a geometric sequence
Determine the common ratio r of the Sequence.
1, 4, 16, 64, 256,

19. Problem Situation: The Brown Tree Snake
The Brown Tree Snake is responsible for entirely wiping out over half of Guam’s native bird and lizard species as well as two out of three of Guam’s native bat species. The Brown Tree Snake was inadvertently introduced to Guam by the US military due to the fact that Guam is a hub for commercial and military shipments in the tropical western Pacific. It will eat frogs, lizards, small mammals, birds and birds' eggs, which is why Guam’s bird, lizard, and bat population has been affected. The data collected on the Brown Tree Snake’s invasion of Guam is shown below.

20. The number of snakes for the first few years is summarized by the following sequence:
1, 5, 25, 125, 625, . . .
What are the next three terms of the sequence?
How did you predict the number of snakes for the 6th, 7th, and 8th terms?
What is the initial term of the sequence?
What is the pattern of change?
Do you think the sequence above is an arithmetic sequence? Why or why not

21. The geometric sequence from the Brown Tree Snake problem (1, 5, 25, 125, ) can be written in the form of a table, as shown below:
The Brown Tree Snake was first introduced to Guam in year 0. At the end of year 1, five snakes were found; at the end of year 2, twenty-five snakes were discovered, and so on…

22. Since we now have a table of the information, a graph can be drawn, where the year is the independent variable (x) and the number of snakes is the dependent variable (y). See below:

23. The graph of the table is NOT a straight line.
The graph is NOT linear in nature
Because the sequence is NOT arithmetic.

24. moves in a growing fashion very rapidly
The graph is…
curved
moves in a growing fashion very rapidly
due to the fact that the common ratio r of this sequence is 5.

25. The curved graph of this problem situation is known as an exponential growth function. An exponential growth function occurs when the common ratio r is greater than one. Tables and graphs make viewing the data from the problem situation easier to see.

29. HW : 5.2

30. Homework Check 5.2 Min: 85, Q1: 90, Med: 100, Q3: 112, Max:120
5+3.50g=40; g=10
2. linear 3. exponential
4. Exponential 5. exponential
6. Exponential 7. linear