Learning Outcomes
By the end of this section, you will be able to:
- Identify and evaluate exponential functions
- Convert from logarithmic form to exponential form
- Convert from exponential form to logarithmic form
- Evaluate functions involving natural logarithms
- Apply the one-to-one property of exponents to solve an exponential equation
- Solve exponential equations of the form [latex]y=Ae^{kt} \ \mathrm{for} \ t[/latex]
Many discrete and continuous probability distributions involve exponential functions. An exponential function is a function involving a constant base and a variable exponent. Suppose you are waiting for a train, which is expected to come soon but might possibly arrive very late. You will learn to model waiting times using a continuous probability distribution. Since the graphs of certain exponential functions take on only positive values and decrease to nearly zero as the variable increases, they are helpful to model situations like wait times. Logarithms are a tool that we can use to solve exponential equations, so they will help us solve problems involving probability distributions modeled by exponential functions.
Recall for success
Look for red boxes like this one throughout the text. They’ll show up just in time to give helpful reminders of the math you’ll need, right where you’ll need it.
