MATH!by:

Donna Ball and Pam

5.2 Exponential Functions & Graphs

• F(x)=ax o x= real #o a>0, a 1

• Graphing Basicso Base e:

f(x)=ex, g(x)=e-x

o Compound Interest: A=P(1+ (r/n))nt

P=initial value, r=rate, n=amount compounded annually, t=time

Ch. 5.2 Example

5.3 Logarithmic Functions & Graphs

• Log Function Equation:o y=logaxo x>0o a=positive #, a 1

• General Rules:o loga1=0, ln1=0

o logaa=1, lne=1

• Log to Exponential:o logax=y x=ay

• Change of Base:o logbM=(logaM/logab)

Ch. 5.3 Example

5.4 Properties of Logarithmic Functions

• Product Rule:o logaMN=logaM+logaN

• Power Rule:o logaMp=p logaM

• Quotient Rule:o loga(M/N)=logaM-logaN

• Logarithm of a Base to a Power:o logaax=x

• Base to a Logarthimic Power:o Alog

ax=x

Ch. 5.4 Example

5.5 Solving Exponential & Logarithmic Equations

• Base-Exponent Property:o ax=ay x=yo a>0, a (can't)=1

• Property of Logarithmic Equality:o logaM=logaN M=No M>0, N>0, a>0, a (can't)=1

Ch. 5.5 Example

5.6 Growth, Decay, & Compound Interest

• Growth Equation:o P(t)=Poekt

o k>0

• Growth Rate & Doubling Time:o KT=ln2o K=(ln2/T)o T=(ln2/K)

• Exponential Decay:o P(t)=Poe-kt

o k>0

• Decay Rate & Half Life:o KT=ln2o K=(ln2/T)o T=(ln2/K)

Ch. 5.6 Example

Ch. 5.6 Example (continued)

7.1 Pythagorean and Sum and Difference

• Basic Identities:

• Pythagorean Identities:

• Sum & Difference Identities:

Ch. 7.1 Example

7.2 Cofunctions, Double-Angle, & Half-Angle

• Cofunction Identities:

• Double-Angle Identities:

• Half-Angle Identities:

Ch. 7.2 Example (cofunctions)

7.3 Proving Trigonometric Identities

• Method 1:o Start with one side and solve for opposite side.

• Method 2:o Solve both sides until they're equal to each other.

• Product-to-Sum Identities:

• Sum-to-Product Identities:

Ch. 7.3 Example