Chapter 3

Chapter 3

1. Toolkits: A.3, A.4

   • a^n
     • a=base n=exponent
   • 3^5
     • 3*3*3*3*3 = 243
   • RULES
     • product rule: multiply=add the exponents
       • 2^3 x 2^6 = 2*2*2 *2*2*2*2*2*2 =2^9
     • Quotient Rule: divide= subtract the exponents
     • power rule: raise a power to another power= multiply the exponents.

2. Exponential growth and decay

   • When given a % you must add 1 to the growth factor
   • Growth: f(x)=Ca^x
   • Decay: f(x)=Ca^x
   • Constant rate of change: SLOPE
   • Later/Initial
     • Less than 1 is DECAY
     • more than 1 is GROWTH
   • HALF LIFE: a= 1/2
     • Half life: The time it takes for half the atoms to decay
   • Compounding interest
     • A= P(1+ r/n)^nt
     • Compounding Continuously: e= 2.718281828...
       • A=Pe^rt
       • Annual Percentage Yield: (A+ r/n)^nt -1

3. Exponential VS. Linear

   • Exponential: Doubling, multiplying by 2

4. Comparing Linear and Exponential Growth

   • Rate of Change: f(x+1) - f(x)

5. LOGS

   • what exponent is needed to go from a base of "a", to a value of "x"
     • Change of base: log(parenthesis) / log(base)
     • log_6(36) = a
       • 6^a= 36 base: 6 solution: a=2