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MATH!

MATH!. by: Donna Ball and Pam. 5.2 Exponential Functions & Graphs. F(x)=a x x= real # a>0, a 1 Graphing Basics Base e: f(x)=e x , g (x)=e -x Compound Interest: A=P(1+ (r/n)) nt P=initial value, r=rate, n=amount compounded annually, t=time. Ch . 5.2 Example.

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MATH!

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  1. MATH! by: Donna Ball and Pam

  2. 5.2 Exponential Functions & Graphs • F(x)=ax • x= real # • a>0, a 1 • Graphing Basics • Base e: • f(x)=ex, g(x)=e-x • Compound Interest: • A=P(1+ (r/n))nt • P=initial value, r=rate, n=amount compounded annually, t=time

  3. Ch. 5.2 Example

  4. 5.3 Logarithmic Functions & Graphs • Log Function Equation: • y=logax • x>0 • a=positive #, a 1 • General Rules: • loga1=0, ln1=0 • logaa=1, lne=1 • Log to Exponential: • logax=yx=ay • Change of Base: • logbM=(logaM/logab)

  5. Ch. 5.3 Example

  6. 5.4 Properties of Logarithmic Functions • Product Rule: • logaMN=logaM+logaN • Power Rule: • logaMp=plogaM • Quotient Rule: • loga(M/N)=logaM-logaN • Logarithm of a Base to a Power: • logaax=x • Base to a Logarthimic Power: • Alogax=x

  7. Ch. 5.4 Example

  8. 5.5 Solving Exponential & Logarithmic Equations • Base-Exponent Property: • ax=ayx=y • a>0, a (can't)=1 • Property of Logarithmic Equality: • logaM=logaNM=N • M>0, N>0, a>0, a (can't)=1

  9. Ch. 5.5 Example

  10. 5.6 Growth, Decay, & Compound Interest • Growth Equation: • P(t)=Poekt • k>0 • Growth Rate & Doubling Time: • KT=ln2 • K=(ln2/T) • T=(ln2/K) • Exponential Decay: • P(t)=Poe-kt • k>0 • Decay Rate & Half Life: • KT=ln2 • K=(ln2/T) • T=(ln2/K)

  11. Ch. 5.6 Example

  12. Ch. 5.6 Example (continued)

  13. 7.1 Pythagorean and Sum and Difference • Basic Identities: • Pythagorean Identities: • Sum & Difference Identities:

  14. Ch. 7.1 Example

  15. 7.2 Cofunctions, Double-Angle, & Half-Angle • Cofunction Identities: • Double-Angle Identities: • Half-Angle Identities:

  16. Ch. 7.2 Example (cofunctions)

  17. 7.3 Proving Trigonometric Identities • Method 1: • Start with one side and solve for opposite side. • Method 2: • Solve both sides until they're equal to each other. • Product-to-Sum Identities: • Sum-to-Product Identities:

  18. Ch. 7.3 Example

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