Chapter 3

Chapter 3

1. Exponential

   • Never touch the x-axis
   • Growth
   • Decay
   • (-10) = -10*-10*-10*-10= 10,000 -10^4= -10*10*10*10= -10,000

2. Equations

   • Half Life F(x)= C(1/2)^x
   • A=(1+(r/n))^nt Compounding Interest
   • A=pe^rt Compounding Continuously
   • APY (1+r/n)^nt -1
   • f(x)=Ca^x

3. Later/initial

4. Chapter 4

   • Instantaneous f(t)=Ce^rt
   • Later/initial
   • 4.1
     • logs = Exponents
     • Examples:
     • log(answer)/log(base)
   • 4.2
     • Example:
     • Condensing: no fractional exponents are allowed so, change to a root
   • 4.3
     • pH=-log[H+]
       • 1.) divide by -1 2.) move the base to the exponent
     • The Decibel Scale B=10*log(I/10^-12)
     • Richter Scale M=log(I/S)
   • 4.4
     • Ln = "e"
     • A=Pe^rt
     • Instatanious
       • f(x)= Ce^rt
   • 4.5
     • Getting information from a model
     • Applications
       • Example; how long would it take to invest #? You would take the formula and set it equal to that #

5. Log_21 (21)^-9y = -9y The base and exponent cancel each other out

6. -53^0 = -1

7. 64^1/3 = 3(square root of) 64 = 4

8. f(x)=45(1.03)^x

   • growth
   • Rate as a %: 3% Rate as a Decimal .03
   • Factor: 1.03

9. 3.2

10. 3.3

    • Is the decay linear or exponential?
      • Multiplying = exponential
        • Half remains = exponential (half life)
      • Decreasing by a # = linear
      • Decreasing by a % = exponential

11. 3.4

    • Exponential funtions moves towards or away from the x-axis but never touch
      • Growth: moves away Decay : moves towards
      • The negative reflects over the x axis

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