# Exponentials and Logs by Kaelin C and Nicole H

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Exponentials and Logs by Kaelin C and Nicole H

## 1. Graphing

### 1.1. Parent Function

1.1.1. b^x

1.1.1.1. Notes from 3/5

### 1.2. Growth vs Decay

1.2.1. b<1 = decay and b>1 is growth

1.2.1.1. Notes from 3/5

### 1.3. Asymptote

1.3.1. is k and is horizontal

1.3.1.1. notes from 3/5

### 1.4. Transformations and Flips

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

1.4.1.1. notes from 3/5

1.4.2. a is vertical flip

1.4.3. c is horizontal flip

1.4.4. h is left and right

1.4.5. k is up and down

## 2. Solving Exponents without logs

### 2.1. Change to common base

2.1.1. solve using exponents of bases to find x

2.1.1.1. paper notes from 3/13 & quiz of Intro to logs

2.1.1.2. same base and equal means exponents are equal

## 3. Logs

### 3.1. Definition

3.1.1. the exponent that I must take the base to in order to get the arguement

3.1.1.1. notes from 3/14

### 3.2. parts of a log

3.2.1. log(base as subscript)(argument)

3.2.1.1. "log base _ of _ is _"

3.2.1.1.1. notes from 3/14

### 3.3. without calculator

3.3.1. make it base to the x power equals the argument

3.3.1.1. exponent chart

3.3.1.2. notes from 3/14

### 3.4. with calculator

3.4.1. hit math alpha math then plug in base and argument

## 4. More equations with logs

### 4.1. logbx = y -> b^y=x

4.1.1. Paper notes from 3/15

### 4.2. Isolate base

4.2.1. inverse operations to cancel out

4.2.1.1. PEMDAS

4.2.1.1.1. paper notes 3/15

### 4.3. use logs

4.3.1. if exponent is equation, find the log that it will be equal to

4.3.1.1. paper notes 3/15

## 5. Applications

### 5.1. half life

5.1.1. how long it takes the thing to half

5.1.1.1. P=P0(.5)^t/h

5.1.1.1.1. packet notes 3/21

5.1.1.1.2. P0 is starting amount and t is time passed and h is half life

### 5.2. Exponential model: ab^x

5.2.1. a= starting value

5.2.2. b=growth/decay factor

5.2.2.1. Notes from 3/19

5.2.2.2. growth = 1 + r & decay = 1 - r

5.2.3. x = time passed

### 5.3. Continuous

5.3.1. change exponentially at a continuous rate

5.3.1.1. P=P0e^rt

5.3.1.1.1. packet notes 3/21

5.3.1.1.2. P0 is starting point and e is Euler's number and r is growth/decay rate and t is time passed