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CCM1 Unit 5

+Warm Up 1 – January 24th

+Homework Check

1. 2. -18

3. Score = Dependent, Time = independent

4. M = 1 5. x < -5

6. 10 +6y 7. y=2x+5

8. x=

+Exponent Rules Review

Exponents are a “short-hand” way of multiplying the same quantity over and over.

Example:

X4 = (x)(x)(x)(x)

+Try Some: Expand the following

43

Y4

X2y5

w6z1

+Using Exponents to simplify

Write using exponents

x*x*x*x

2*2*2*2*x*x*x*y*y

3*3*3*4*4*4*4*x

+Zero as an exponent

Anything with an exponent of zero equals 1.

Ex x0 = 1

60 =

Y0 =

+Negative Exponents

When you have a NEGATIVE exponent you turn it POSITIVE and FLIP it.

EX. x-3

+Try Some

+Multiplication

When multiplying like bases you ADD exponents

Ex: x4x2

+Try some!

x3x4

y3x4y7

z3y2x5z5y6x10

+Exponents of Exponents

When you have an exponent of an exponent you MULTIPLY

EX: (x4)3

+Try Some!

(x)5

(x2y4)5

(2x3)6

+Division

When you divide like bases you SUBTRACT exponents

Fix any negatives if they show up!!

+Try Some

+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, . . .

+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, 16, 64, 256, 1024 . . .

+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.

+ 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

+Complete the rest of the worksheet

HW : 5.2