MATH! by: Donna Ball and Pam. 5.2 Exponential Functions & Graphs F(x)=a x o x= real # o a>0, a 1...
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Transcript of MATH! by: Donna Ball and Pam. 5.2 Exponential Functions & Graphs F(x)=a x o x= real # o a>0, a 1...
![Page 1: MATH! by: Donna Ball and Pam. 5.2 Exponential Functions & Graphs F(x)=a x o x= real # o a>0, a 1 Graphing Basics o Base e: f(x)=e x, g(x)=e -x o Compound.](https://reader035.fdocuments.us/reader035/viewer/2022062517/56649e875503460f94b8b3c8/html5/thumbnails/1.jpg)
MATH!by:
Donna Ball and Pam
![Page 2: MATH! by: Donna Ball and Pam. 5.2 Exponential Functions & Graphs F(x)=a x o x= real # o a>0, a 1 Graphing Basics o Base e: f(x)=e x, g(x)=e -x o Compound.](https://reader035.fdocuments.us/reader035/viewer/2022062517/56649e875503460f94b8b3c8/html5/thumbnails/2.jpg)
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
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Ch. 5.2 Example
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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)
![Page 5: MATH! by: Donna Ball and Pam. 5.2 Exponential Functions & Graphs F(x)=a x o x= real # o a>0, a 1 Graphing Basics o Base e: f(x)=e x, g(x)=e -x o Compound.](https://reader035.fdocuments.us/reader035/viewer/2022062517/56649e875503460f94b8b3c8/html5/thumbnails/5.jpg)
Ch. 5.3 Example
![Page 6: MATH! by: Donna Ball and Pam. 5.2 Exponential Functions & Graphs F(x)=a x o x= real # o a>0, a 1 Graphing Basics o Base e: f(x)=e x, g(x)=e -x o Compound.](https://reader035.fdocuments.us/reader035/viewer/2022062517/56649e875503460f94b8b3c8/html5/thumbnails/6.jpg)
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
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Ch. 5.4 Example
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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
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Ch. 5.5 Example
![Page 10: MATH! by: Donna Ball and Pam. 5.2 Exponential Functions & Graphs F(x)=a x o x= real # o a>0, a 1 Graphing Basics o Base e: f(x)=e x, g(x)=e -x o Compound.](https://reader035.fdocuments.us/reader035/viewer/2022062517/56649e875503460f94b8b3c8/html5/thumbnails/10.jpg)
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)
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Ch. 5.6 Example
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Ch. 5.6 Example (continued)
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7.1 Pythagorean and Sum and Difference
• Basic Identities:
• Pythagorean Identities:
• Sum & Difference Identities:
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Ch. 7.1 Example
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7.2 Cofunctions, Double-Angle, & Half-Angle
• Cofunction Identities:
• Double-Angle Identities:
• Half-Angle Identities:
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Ch. 7.2 Example (cofunctions)
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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:
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Ch. 7.3 Example