In this module you will solve differential equations that model exponential growth and decay. The applications you will study arise in the various fields of finance, thermodynamics and electronics. The differential equation y' =ky, which describes a quantity that changes at a rate proportional to itself, is the model for continuously compounded interest and charge on a capacitor which is closely related to Newton's Law of Cooling.

Lesson Index:

19.1 - Continuously Compounded Interest

19.2 - Newton's Law of Cooling

19.3 - Charge on a Capacitor

After completing this module, you should be able to do the following:

• Find doubling times for continuously compounded interest
• Find future values for investments that accrue interest continuously
• Solve problems involving heating and cooling liquids
• Solve a differential equation to determine the charge on a capacitor
• Find the half-life of the charge on a capacitor