Exponential and Logarithmic Functions

Exponential and Logarithmic Functions

1. Apply

   • Interest
     • Money
       • Continuous
         • A=Pe^rt
       • Compound
         • A=P(1+r/n)^rt
   • Exponential Growth
     • Continuous
       • N=Noe^kt
     • Compound
       • N=No(1+k)^t
     • Decay
       • k=-0.5
   • Properties
     • Power
       • logbm^n
         • nlogbm
     • Division
       • logb(n/m)
         • logbn-logbm
     • Product
       • logbnm
         • logbn+logbm
     • One on One
       • LogmA=LogmB
         • A+B

2. Functions

   • Exponetial
     • F(x)=b^x
   • Logarithmic
     • F(x)=logbX

3. Graph

   • Exponential
     • (0,1), (1,b)
   • Logarithmic
     • Transformation
       • Parent Function
         • HDRV
           • Two Key points
             • Plot Points
     • (1,0), (b,1)
     • With out Calculator
       • Exponential Form
         • Insert Y value
           • Make a table
             • Plot Points
         • y=logbX equivalent X=b^y

4. Solve

   • Logarithmic
     • Single Log
       • Isolate Log
         • Convert to exponential
     • Mulltiple Logs
       • Condense
         • Use one on one property
   • Exponential
     • Rewrite terms of same base
       • use one on one property
     • Isolate exponential
       • use inverse log with same base to get the variable out of exponential

5. Change of Base rule

   • logb(a)=logx(a)/logx(b)