Rules of Exponents

***When you're in doubt, expand it out.

Add
1. Add terms with the same exponents. Just add coefficients, not exponents.

Multiply
2. Multiply coefficients and add the exponents.

*** If I forget the rule, when in doubt, expand it out.

Division
3. A. Expand it out (When in doubt, expand it out)
    B. Cancel out like variable on top that are the same on the bottom (when you're done, make it one)

Multiply
4. Multiply the terms if they have the same exponents

L-62

(x^3)^4

(y^7)^2

(x^4)^6

**When you are in doubt, you expand it out

R and L 63 Quadratics

L-61:

Public Record

Area: Count the values add them
=> Add the big square= x^2, add the strip=x, and add the chips= 1.


Dimensions: Count the x strips and add to the x of the big square for each side.

If I gave you some random area, is it possible that you could determine the dimensions? 


Rules:

x^2+7x+12

3 and 4
3+4=7 Total x's
3 x 4=12 chips

If you multiply 6 x 1= 6 and if you add 6 + 1=7

If you have one x^2 and 9 single squares. How many different dimensions can you create using as many x strips as you want.

Quadratics

Staking a claim

Pretend you are on Mars. There are new precious metals found and Ally wants to make a claim. She wants to protect her claim and use laser fencing.

She has 20 meters of laser fencing, how can she represent a rectangular figure in a variety of ways with the laser fencing?


A. area=16

B. area= 21

C. area=9

 

How can we make this into a table? 

-side length, perimeter, area

Length      Area

R-55 Exponents

R-55 Exponents 

Scenario 1-

6000 , 2, 10,000,
6000   2  10, 000

π, a, b^2

π  a  b^2

3

4  

3

4

**All equal 1

Scenario 2-

16, 8, 15, 3*3,  5*3    , 7*2*5

8   16  3   3*4   3*2*5  5*7

**

L-55 Generalizations
 1. Fractions are division problems so if you divide a number by itself it equals 1.

 

R-54 Decay Factor/Rate

Decay Factor- is what is left

Decay Rate-is what is taken away

Decay factor + Decay rate= 1

y= a(df) ^x

a=y-intercept
df= decay factor less than 1

Table- divide lower # by upper #

x  y

1  2
2  1

1 divided by 2= 1/2 or .5
Less than 1
decay factor


HOMEWORK
L-53/L-54
pg. 69 #8, #10-13, 14, 15, 17

What is Growth Factor?

What do we think growth factor is?

*# that tells you how much it goes up by everytime
*Graph-the line, the differences between each point
*Table-Difference between the points
*Equation-y=n^x   (The class is still unsure which is the growth factor. x or n?)

ABC Problems

A

Lake Victoria
S.A.=25,000,000
Initially Covers=1,000 sq.feet
(doubles every month)

B

Mold
M=50 (3^d)
M=area of mold in sq.millimeters
d=days

C

 

Growth Factor: What tells a # how fast it will grow

1. Math stuff you know

2. Question 

-y-intercept

-x-intercept

3. Real Life implications of problems