Freeman Chapter 14

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Freeman Chapter 14 by Mind Map: Freeman Chapter 14

1. 14.1 Exponential Functions

1.1. A = P(1+r/n)^n*t or A = Pe^rt A - P - Principal r - interest rate n - times per year t - time (how long)

1.2. Graphing 1. Find x/y 2. Plot points 3. Graph - Domain - Range - Horizontal Asymptote

2. 14.2 Functions

2.1. Composite

2.1.1. ( f o g )( x) = f (g (x)) 1. F into G or vice versa

2.2. Inverse

2.2.1. f ( f ^-1 (x)) = x and f ^-1 ( f (x)) = x 1. Switch x and y 2. Solve for y

3. 14.3 Logarithmic Functions

3.1. log ,a, x = n <--inverse--> a^n = x

4. 14.4 Properties of Logarithms

4.1. log base (b) (xy) = log base (b) x + log base (b) y log base (b) (x/y) = log base (b) x - log base (b) y log base (b) (x^n) = n log base (b) x log base (b) x = log base (a) x / log (a) b log base (b) 1 = 0 log base (b) b = 1 log base (b) b^2 = 2 log base (b) b^x = x (b) log base (b) x = x. log base (a) b = 1/log base (b) a

5. 14.6 Exponential Growth/Decay

5.1. Radiocarbon Dating

5.1.1. A=A_0e^kt

5.1.2. A = A_0e^-0.000121t

5.1.3. Word Problems Check for what information you have Find Rate first Then find answer

6. 14.5 Solving

6.1. Exponentials

6.1.1. 1. Turn exp. form to log form 2. Solve for x (a=p(1+r/n)^nt) (a=pe^rt)

6.2. Logarithms

6.2.1. 1. Combine 2. Exponentiation (*wink) or ln=e 3. solve for x 4. Check for negative of log's