Logs & Exponents; Anita and Whitney

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Logs & Exponents; Anita and Whitney

1. Graphing Exponent

1.1. Asymptote

1.1.1. Y-Interecept

1.1.1.1. Notes; 3/5/19

1.2. Growth/Decay

1.2.1. determined by base; if greater than 1, its growth; if its less than 1, its decay

1.3. End Behavior

1.3.1. Notes; 3/5/19

1.4. Increasing/Decreasing

1.4.1. left to right

1.4.1.1. Notes; 3/5/19

1.5. Shape/Curve

1.5.1. specific to this function

1.5.1.1. Notes; 3/5/19

1.6. Parent Function

1.6.1. anchor point; (0,1)

1.6.1.1. Notes; 3/5/19

1.6.2. asymptote; y=0

1.6.2.1. Notes; 3/5/19

1.6.3. f(x)=ab^cx-h+k

1.6.3.1. Notes; 3/5/19

1.7. Vertical/ Horizontal/ Negative Flip

1.7.1. determined by negative in front of "b" and "x".

1.7.1.1. Notes; 3/5/19

2. Solving exponents without Logs

2.1. If bases are equal, then the exponent are equal

2.1.1. Notes; 3/12/19

3. Logarithms

3.1. Log base "b" of "argument"= "exponent"(logbx=y)

3.1.1. Notes; 3/14/29

3.2. the exponent that I must take the "base" to in order to get the "argument"

3.2.1. Notes; 3/14/19

3.3. log without a base; Common Log; base is 10

3.3.1. Notes; 3/14/19

3.4. log with a base of "e"; Natural Log

3.4.1. Notes; 3/14/19

4. More equations with Logs

4.1. Can't make the base equal, isolate the base/ exponent, convert to Log(logbx=y <--> b^y=x)

4.1.1. Notes; 3/15/19

5. Applications

5.1. Exponential model

5.1.1. ab^x; a= starting #, b=the rate, x= time/how long it takes.

5.2. Half Life

5.2.1. Decay model, how much it takes a quantity to half in size.

5.2.2. a(1/2)^x/H

5.2.2.1. x= the time gone by.

5.2.2.2. H= the time it takes to half.

5.3. Continuous

5.3.1. specifically says "Continuously"

5.3.2. P= Poe^rt; e= Euler's number, r= growth/decay % in decimal, t= time