Chapter 3 & 4

Chapter 3 & 4

1. COMPOUNDING INTEREST

   • A=P(1+r/n)^nt
   • COMPOUNDING CONTINUOUSLY
     • A=Pe^rt

2. LOGS

   • log9(729) = m
     • 9^m = 729 m= 3
   • Change of base logaX/logaB
   • Laws of logs
     • multi. = expand in addition
       • division = expand in subtraction
         • exponent = move exponent in front of log
   • pH scale
     • pH= - log[H+]
     • Decibel scale
       • S= k* log [I/I0]
     • Richter scale
       • M= log(I/S)

3. NATURAL EXPONENTIAL

   • f(x) = e^x
   • NATURAL LOG
     • f(x) = ln(x) = loge (x)
   • Exponential growth decay
     • f(x) = Ca^x
     • Instantaneous growth/decay
       • f(x) = Ce^rx
         • rate of growth or decay = r= ln(a)

4. EXPONENTS

   • Multiplying powers of same # means add exponents
     • 2^3 x 2^6 = 2^9
   • Dividing same powers means subtract exponents
     • 5^5/5^2 = 5^3
   • Power to anther power means multiply exponents
     • (6^3)^2
   • product to power, raise each factor to power
     • (7x)^3 = 7^3 x^3 = 343x^3
   • Quotient to power, numerator and denominator to power
     • (3/8)^4 = 3^4/8^4 = 81/4096

5. HALF LIFE

   • Decay factor is 1/2
     • Half life of cesium is 30 yrs, we have a 100g sample
       • 100(1/2)^x (X is the number of half lifes plugged in)

6. Exponential growth/decay

   • growth: greater than 1 (f(x)=2^x
     • decay: less than 1 (f(x0=1/2^x)