Unit 2

Unit 2

1. Chapter 3

   • 3.1 Exponential growth & Decay
     • Exponential Growth
       • The growth/decay Factor
         • f(x)=10 x 2^x
           • 10 is starting point
           • 2^x is growth factor
         • r=f(x+1)-f(x)/f(x)
           • r=a-1or 1+a
         • f(x)=Ca^x
           • a<1
       • f(x)=Ca^x
         • a>1
   • 3.2 Exponential Models: Comparing Rates
     • Changing Time Period
       • Daily: a Weekly: a^7
       • Weekly: b Daily: b^1/7
       • Monthly: c Yearly: c^12
       • Yearly: d Monthly: d^12
     • Compound Interest
       • A(t)=P(1+r/n)^nt
   • 3.3 Comparing Linear and Exponential Growth
     • Average Rate of Change & Percentage Rate of Change
       • Percentage Rate: r=f(x+1) - f(x)/f(x)
     • Linear
       • f(x)= b+mx
         • Initial Value: b
     • Exponential
       • Exponential
         • f(x)= Ca^x
         • Initial Value:C

2. Chapter 4

   • 4.1 Logarithmic Functions
     • Log Base 10
       • log(x)=y if 10^y=x
     • Log base a
       • Loga(x)=y if a^y=x
   • 4.2 Laws of logarithms
     • Law of Logarithms
       • Log(AB)=logA+LogB
       • Log(A/B)=LogA - LogB
       • Log(A^C)=CLogA
     • Change of Base
       • Logb(x)=Log(x)/Log(b)
   • 4.3Logarithmic Scales
     • Logarithmic Scales
       • Linear Scales: Each successive mark on the scale corresponds to adding a fixed constant
       • Logarithmic scales: Each successive mark on the scale corresponds to multiplying by a fixed factor
     • The pH Scale
       • pH=-log(h^+)
     • The Decibel Scale
       • S=Klog(I/I9(subcript)0)
     • The Richter scale
       • M=logI/S
   • 4.4 The natural Exponential and Logarithmic Functions
   • 4.5 Exponential Equations