Chapter 3 and 4

Chapter 3 and 4

1. 3.1 Exponential Grow and Decay

   • Both growth and decay models are expressed with the same model
     • f(x)=Ca^x
     • Decay= 0<a<1
     • Growth= a>1
   • Linear vs. Exponential
     • Linear
       • Contant rate of change y=20x+7
     • Exponential
       • Multiplying y=Ca^x
   • Half Life
     • f(x)=C(.5)^x

2. 3.2 Exponential Models: Comparing Rates

   • Computing Interest
     • A=P(1+r/n)^nt
       • A= Amount in the account P= Principal (the amount initially deposited) r= Annual interest rate written as a decimal&nbsp; n= Number of times the interest is compounded in one year t= Time the investment is made for, in years
   • Compounding Continuously
     • A=Pe^rt
       • e=2.718281828
   • Annual Percentage Yield
     • (1+r/n)^nt -1

3. 3.3 Comparing Linear and Exponential Growth

   • Rate of Change
     • f(x+1)-f(x)
   • Percent Rate of Change
     • r=a-1

4. 3.4 Graphs of Exponential Functions

   • Decay
     • 0<a<1
       • Moving towards the X- Axis
   • Growth
     • a>1
       • Moving away from the X-Axis

5. 4.1 Logarithmic Functions

   • Logarithms Base
     • LOGaX=Y if and only if A^y=X
   • Change of Base Formula
   • Basic Properties of Logarithms

6. 4.2 Laws of Logarithms

   • Laws

7. 4.4 Natural Exponential and Logarithmic Functions

   • Natural Exponential Function
     • f(x)=e^x
   • Natural Logarithm Function
     • f(x)=ln(x)=LOGe(X)
   • Instataneous Growth and Decay
     • r=ln(a)

8. 4.5 Exponential Equations: Getting Information From a Model

   • Application of Exponentials and Logarithms
     • EXPONENTIAL- 7.5 billion people and is increasing by 1.13% every year
       • 2016 to 2050&nbsp; 7.5(1+.013)^34 =10.99
     • LOGARITHM- Invest $10,000 and desposites that pays 12% annually and is compounded every 6 months
       • A=10,000(1+.12/2)^2xt After 3 years &nbsp;(t)=3 =14,185.19

9. 4.3 Logarithmic Scales

   • PH Scale
   • Decibel Scale
   • Richter Scale

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