Math 141 Chapter 3 and 4

Math 141 Chapter 3 and 4

1. Chapter 3

   • Rate of change f(x+1)-f(x)
   • Linear and exponential growth
     • Percent rate of change r=a-1
   • Graphs of exponential functions
     • Domain (-x,x) Range (0,x)
   • Exponential growth/ decay
     • f(x)= Ca^x where a>1
       • a>1= Decay a<1=Growth
   • Exponential models
     • Compounding interest A=P((1+(r/n))^nt

2. Chapter 4

   • Logarithms Base a
     • positive a: log base a of x equals y a to the power of y equals x
   • Law of logs
     • logb(mn)=logb(m)+logb(n) logb(m/n)= logb(m)-logb(n) Logb(m^n)=n*logb(m)
   • Log scales
     • pH scale pH= -log[H+]
     • dB scale S=K*log(I/10^-12)
   • Natural Exponential & Logarithm Functions
     • Natural exponential f(x)= e^x
     • Natural log f(x)=ln(x)= log base e (x)
     • Exponential growth/ decay
       • f(t)= Ce^(rt)
       • f(x)= Ca^x
   • Exponential equations
     • Convert exponential to logs convert logs to exponential