Chapter 3

Chapter 3

1. 3.1: Exponential Growth/Decay

   • 3.2: Exponential Models and Comparing Rates
     • 3.5: Fitting Exponential Curves to Data
       • percentage rate of change
       • y=ab^x
     • exponential growth
       • f(t)=Ca^kt=Cb^t
     • compound interest
       • A(t)=P(1+r/n)^nt
   • exponential growth and decay are modeled by f(x)=Ca^x
     • the variable x is the number of time periods
     • the base a is the growth and decay factor
     • the constant C is the initial value of f
   • a is always greater than 0 and can never be 1

2. 3.3: Comparing Linear and Exponential Growth

   • 3.4: Graphs of Exponential Functions
     • exponential function with base
       • f(x)=a^x
       • a is greater than 1
     • the domain is all real numbers and the range is all positive real numbers
     • the line y=0 (x-axis) is a horizontal asymptote of f
     • if a is greater than 1, the graph increases
     • if a is less than 1, the graph decreases
   • constant percent rate of change
     • (x+1) or x
   • logistic growth model
     • f(x)=C/1+b*a^-x
       • a is always greater than 1