Chapter 3 & 4

Chapter 3 & 4

1. Chpt. 3 Sect 1

   • exponential  decay and growth 
   • Exponential growth
     • f(x)=Ca^x
       • X= time  a= Growth factor  C= initial value
       • Exponential decay
         • 0<a<1
     • a>1

2. Chpt. 3 Sect 2

   • Exponential Models: Comparing Rates&nbsp;
   • Annual Percentage rate
     • (1+ r/n)^n*1
       • r= rate&nbsp; n=time&nbsp; Annually= 1&nbsp; Semi-annually= 2&nbsp; Quarterly= 4&nbsp; Monthly= 12 Weekly= 52&nbsp; Daily=365
   • Compound Interest
     • P(1+r/n)^n*t

3. Chpt. 3 Sect 3

   • Average rate of change
     • f(b)-f(a)/b-a
   • percentage rate of change
     • f(x+1)-f(x)/f(x)

4. Chpt. 3 Sect 4

   • Graphs of Exponential Functions
   • exponential function with a base
     • f(x)=a^2
       • a>0 & a=1

5. Chpt. 4 Sect. 1

   • Logarithmic Functions&nbsp;
   • Logarithmic base 10
     • log10 X=Y
       • if and only if 10y=x
   • Powers of 10
     • 10^-4= -4&nbsp; 10^-3=-3 10^-2=-2 10^-1=-1 10^0=0 10^1=1 10^2=2 10^3=3 10^4=4
   • logarithm base
     • loga x=y
     • log function w base
       • f(x)= loga X
   • Basic properties of logarithms
     • loga 1=0&nbsp; loga a=1&nbsp; loga a^x=x a^logax =x

6. Chpt. 4 Sect 2

   • Laws of Logarithms&nbsp;
   • Laws of logarithms
     • lawa AB= loga A+ loga B loga A/B= logaA - loga B loga Ac = ClogaA&nbsp;
     • log(12/n)
       • log12-logn
   • change of base formula
     • logb x = logax/logab

7. Chpt. 4 Sect 3

   • Logarithmic Scales&nbsp;
   • Linear Scale
     • fixed marks on the scale corresponds to an adding a fixed constant.
   • log scale
     • each mark on the scale corresponds to multiplying by a fixed factor.
   • pH scale
     • pH less than 7 is acidic
     • pH greater than 7 is basic
     • 7 is neutral
   • The Decibel Scale
     • S= k*log(l/lo) Io=10-12W/m2 B=10*log (I/Io)
   • Richter Scale
     • log (I/S)

8. Chpt.4 Sect 4

   • Natural Exponential and Logarithmic Functions&nbsp;
   • natural logarithm function
     • f(x)= logex=intx
   • natural exponential function
     • f(x)= ex
   • compounded continously
     • A(t)=Pe^rt
   • 25000(1+0.06/4)^(4*10)
     • $25000 is invested at a rate of 6% per year, invested in 10 years and is compounded quarterly&nbsp;
     • $45350.46

9. Chpt. 4 Sect 5

   • exponential equations&nbsp;
   • 2^x=16
     • log2^2x=log2^16
       • x=log2^2^4
         • x=4

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