1. Math Refresh Evaluating Equations We have 4 basic relatiojnships
Y= k X Direct Proportion
Y=k/X Inverse proportion
Y=k Xn Direct Exponential
Y=k/ Xn Inverse Exponential

2. Direct Proportion Y=kX This equation of a straight line with slope k
As X increases, Y increases by same proportion
If you increase X by 10%, Y will increase 10%
If you double X, you will double Y
Very straight forward

3. Inverse proportion Y= k / X
If you increase X by 10%, Y will decrease by 10%
If you double X, Y will decline by factor of 2
Y and X move in opposite direction, one increases, the other decreases

4. Direct Exponential Y=kXn The Exponent n is very powerful
If n=2 and you double X, then Y increases by factor of 4
If n= 3 and you double X, Y increases by factor of 9

5. Inverse Exponential Inverse Exponential Y=k/ Xn
Again, n is very powerful, but now it increases the effect of X in the denominator Y X

6. Math Refresher Inverse Relationship
Y= 5/X Y declines in proportion to X increasing
Y =5/X2 Y declines much faster with X increasing ( Inverse Squared relation)
For example when x=1, then Y=5
But when x=2, then Y = 1.25 or one fourth what is was when x =1
What is Y when x=3?

7. Powers of 10 There are 31,557,600 seconds per year
Light travels at 300,000,000 meters per second
Distance traveled in one year
9.47 x 1015 meters
x 107 x 3.00 x 108 = 9.47 x 1015 meters

8. Powers of 10 Scale of Universe 1.5 x 1026 meters
Scale of Hydrogen Nucleus
1x meters
The range of Powers of 10 from atomic scale to
Is captured by 41 powers of 10

9. Powers of 10 Rules Multiplication ADD the exponents Division
Move the Exponent terms from denominator to numerator and change the sign of exponent
Then proceed as with Multiplication, ie, add the exponents

10. Example
E= MC2
Solve for Mass of an electron if its mass energy is 8.19 x joules and C = 3.0 x 108 m/s
M=E/C2 = 8.19 x / (3.0 x 108)2
= 8.19 x / (9.0 X 1016 )
= .91 x x 10-16
= .91 x 10-30
= 9.1 x kg

11. Math Refresher Evaluate in Powers of 10 notation
(30x 80,000,000,000)/.0004
= 3.0 x 101 x 8 x / (4 x )
= 6 x 101 x x 104 = 6 x 1015
0.0001/(60,000 x 200)
= 1 x 10-4 / (6 x x 2 x 102 )
= .08 x x x 10-2 = .08 x = 8 x 1012

12. Algebra
a/b = c/d
Must be able to solve for any one of the four if you know the other three
So: a = bc/d
b = ad/c
c = ad/b

13. Math Refresher
For further review, in appendix A of Text