Linear Programming

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:	-5,4		0,6		0,4
Constraints	Objective Function:
x ≤  5 y ≥ 4 -2x +5 y ≤ 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:
x ≥ 0 y ≥ 0 4x + 4y ≤ 20 x + 2y ≤ 8	C=8x+7y	C=35		C= 0		C=37		C=64 =

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

Arithmetic and Geometric

Sequence- Is an ordered list of terms or elements.

 

Arithmetic sequence formula- In an Arithmetic Sequence the difference between one term and the next is a constant. Also called the Common Difference.

 

Geometric sequence formula- In a Geometric Sequence each term is found by multiplying the previous term by a constant. Also called the Common Ratio.

Example:

2, 4, 8, 16, 32, 64, 128, 256, ...

This sequence has a factor of 2 between each number. Each term (except the first term) is found by multiplying the previous term by 2.

Finite sequence- Is a function with domain 1,2,3.

Infinite sequence- Is a function with domain 1,2,3,4.... etc.

Series- Is the sum of a sequence.

Explicit formula- Each domain is an answer not based on any values.

Recursive Formula- Each domain is a answer based on a previous answer.

Graphing Exponential Equations

Graphing Exponential Equations

Graphing Exponential Growth/Decay

1. Create the Parent Graph.

2. Identify A,H,K.

3. Create your new T-Chart.

• Domain: All real #'s.
• Range: y>k; when a is positive. y<k; when a is negative.
• Asymptote: y=k.

4. Draw Asymptote.

5. Graph new points.

• Exponential Formula: y=a×b^x-h+k
• a = multiplier.

a>1 = stretch
0<a<1 = compression
a< 0(negative) = flipped over x-axis.

• b = base

b>1 = whole #, growth, always increasing.

0<b<1 = fraction; decay, always decreasing.

B is never negative only the multiplier is.

• h = lf/rt; opposite
• k = up/dn

Compound Interest

Compound Interest

Interest calculated on the initial principal and also on the accumulated interest of previous periods of a deposit or loan. Compound interest can be thought of as “interest on interest,” and will make a deposit or loan grow at a faster rate than simple interest, which is interest calculated only on the principal amount.



 = [P (1 + i)ⁿ] – P

= P [(1 + i)ⁿ – 1]

Compound Interest = Total amount of Principal and Interest in future (or Future Value) less Principal amount at present (or Present Value)