Chapter 3

Chapter 3

1. Exponential Growth

   • f(x)=Ca^x
   • Base a is the growth factor
   • The graph goes up

2. Chapter 4

   • Log base 10
     • log10 x=y or 10^x=x
     • log base 10 is known as common logs
     • if we see a log with a positive exponent then we raise that to the 10
   • Log base a
     • a^x=x
     • log base a of x
   • log function
     • f(x)=logax
   • Laws of logs
     • logaAB=logaA+logaB
     • loga A/B=logaA-logaB
     • logaA^c=ClogaA
   • Expanding and combining logs
     • product or a quotient as a sum or difference of logs
     • reverse process of expanding is combining
   • Change of base formula
     • logbX=logaX/logaB

3. Growth rate

   • r=f(x+1)-f(x)/f(x)
   • the growth rate r is represented as a decimal.
   • a=1+r

4. Exponential decay

   • f(x)=Ca^x
   • postive number less than one
   • a=1+r, negative number
   • graph going down

5. Half-life

   • a=1/2
   • 1600-year decay factor
   • EX: m(x)=50 x (1/2)^x
   • m(x)=C(1/2)^x

6. Compound Interest

   • A(t)=P(1+r/n)^rt
   • r is often referred to as the nominal annual interest rate