4.1 Introduction

· Properties of rational exponents and extension to any real exponent.

 

4.2 The natural exponential function

· Know how the graph of the basic exponential function looks like (domain, range, asymptote).

·Know how to sketch the graph of transformations (shifts, reflections, compressions, stretches) of the basic exponential function. Know how to determine their domain and range.

· Be familiar with the natural exponential function (base e).

· Know how to apply the formulas for compound interest.

 

4.3 Logarithmic functions

· Be familiar with the definition of logarithmic function, including the natural logarithm, ln x. 

· Know how to use the inverse relationship with the exponential function to find values of the log function or to solve simple logarithmic equations.

· Know how the graph of the log function looks like (domain, range, asymptote) and how to sketch transformations of the basic graph.

· Know the arithmetic properties of logarithms (page 295).

· Know how to solve logarithmic equations (remember to always check your solution) and exponential equations.

 

4.4 Exponential growth and decay

· Know how to determine a model for exponential growth or decay given the necessary information (e.g initial value and doubling time or any two points on the graph)

· Know how to find relevant information given the exponential model by plugging in the appropriate value of t or by solving the appropriate exponential equation.