Linear Programming

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Vertices:	0,6		0,0		6,0
Constraints	Objective Function:
x ≥ 0 y ≥ 0 x + y ≤ 6	C=3x+4y	C=24		C=0		C=18

Vertices:	0,6		0,4		-5,4
Constraints	Objective Function:
x ≤  5 y ≥ 4 -2x + 5y ≤ 30	C=2x+5y	C=30		C=20		C=10

Vertices:	0,9.5		0,2		5,2
Constraints	Objective Function:
x ≥ 1 y ≥ 2 6x + 4y ≤ 38	C=7x+3y	C=28.5		C=6		C=41

Vertices:	0,8		0,4		6,8
Constraints	Objective Function:
x ≥ 0 y ≤ 8 -2x + 3y ≤ 12	C=4x+6y	C=48		C=24		C=72

Vertices:	0,5		0,0		2,3		8,0
Constraints	Objective Function: C= 8x +7y
x ≥ 0 y ≥ 0 4x + 4y ≤ 20 x + 2y ≤ 8	C=35	C=0		C=37		C=64

Vertices:	0,4		0,0		4,3		16,0
Constraints	Objective Function: C= 3x + 5y
x ≥ 0 2x+3y ≥ 6 3x - y ≤ 9 x+4y≤ 16	C=20	C=0		C=27		C=48

Compound Interest

Compound Interest: Interest calculated on the initial principal and also on the accumulated interest of previous periods of a deposit or loan.

 

P = principal amount (the initial amount you borrow or deposit)

r  = annual rate of interest (as a decimal)

t  = number of years the amount is deposited or borrowed for.

A = amount of money accumulated after n years, including interest.

n  =  number of times the interest is compounded per year 

    Ex. 1,500 dollars is deposited in the bank paying a yearly interest rate of  4.3% compounded quarterly. what is the balance after 6 years?
P: 1,500
R: 0.043
N: 4
T: 6

Graphing Exponential Equations

Exponential Equation: It is an equation involving exponential functions of a variable.
Exponential Growth: This is a growth whose rate becomes ever more rapid in proportion to the growing total number or size.
  Exponential Decay: It is a Exponential decay is a particular form of a very rapid decrease in some quantity.

 

Arithmetic/Geometric Sequences

     An arithmetic sequence is a sequence in which the difference between each consecutive term is constant.
Ex. 1, 4, 7, 10, 13, 16, 19, 22, 25
       A geometric sequence is a sequence with the ratio between two consecutive terms constant.
Ex. 2, 4, 8, 16, 32, 64, 128, 256