Chapter 3

Chapter 3

1. Exponential growth

   • Ca^x where a>1
   • C = initial value A = growth factor
   • Exponential decay
     • Ca^x where 0<a<1
       • a = 1 + r

2. Growth factor

   • Later/Initial
   • Half-Life = .5, Annually = 1, Monthly = 12, quarterly = 4, Weekly = 52, semiannually = 2, Daily = 365, Hourly = 8,760
   • Compounding interest
     • A=P(1+r/n)^nt
       • A= Amount in account
         • B = Principle
           • r = annually interest rate written as a decimal
             • n = # of times the interest is compounded in 1 yr
               • t = time the investment is made for, in years
     • A = Pe^rt
       • Annual % yield
         • (1+r/n)^nt - 1

3. Rate of change

   • f (x + 1) - f(x)
     • r = a - 1 when r is expressed as a %

4. Linear vs. Exponential

   • avg rate of change = slope
   • growth/decay factor = % rate of change
   • Exponential = * or /
   • Linear = + or -

5. Graphs of Exponential functions

   • f(x) = a^x where a>0