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

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

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

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

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

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?

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 3.15576x 107 x 3.00 x 108 = 9.47 x 1015 meters

Powers of 10 Scale of Universe 1.5 x 1026 meters Scale of Hydrogen Nucleus 1x 10-15 meters The range of Powers of 10 from atomic scale to Is captured by 41 powers of 10

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

Example E= MC2 Solve for Mass of an electron if its mass energy is 8.19 x 10-14 joules and C = 3.0 x 108 m/s M=E/C2 = 8.19 x 10-14 / (3.0 x 108)2 = 8.19 x 10-14 / (9.0 X 1016 ) = .91 x 10-14 x 10-16 = .91 x 10-30 = 9.1 x 10-31 kg

Math Refresher Evaluate in Powers of 10 notation (30x 80,000,000,000)/.0004 = 3.0 x 101 x 8 x 1010 / (4 x 10-4 ) = 6 x 101 x 1010 x 104 = 6 x 1015 0.0001/(60,000 x 200) = 1 x 10-4 / (6 x 104 x 2 x 102 ) = .08 x 10-4 x 10-4 x 10-2 = .08 x 10-10 = 8 x 1012

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

Math Refresher For further review, in appendix A of Text