3.2 Exponential Growth and Decay

By the end of your studying, you should know:
Onscreen applet instructions:
The applet shows the graph of y = Be^{kx}. Use the vertical slider to change k, and the horizontal slider to change B.
ExamplesWe have a 100gallon tank filled with water. Saltwater is being pumped into the tank through two pipes.
A cup of coffee is initially 170 degrees Fahrenheit and is left in a room with ambient temperature 70 degrees Fahrenheit. Suppose that when the coffee is first placed in the room, it is cooling at a rate of 20 degrees per minute. Assuming Newton's law of cooling applies, how long does it take for the coffee to cool to 110 degrees?
The population of fish in a pond is modeled by the differential equation
AppletsCalculator: Values of Elementary Functions
VideosSee short videos of worked problems for this section.
QuizExercisesSee Exercises for 3.2 Exponential Growth and Decay (PDF).Work online to solve the exercises for this section, or for any other section of the textbook. 
Resources on the WebInformation on NewtonBiographical data from St. Andrew's University's Web site Excerpt from W.W. Rouse Ball's "A Short Account of the History of Mathematics"
Information on Leibniz
Calculus Applications

Interesting ApplicationThe forgetting curve appears to be a decaying exponential. 
3.1 Modeling with Differential Equations  Table of Contents  3.3 Separable Differential Equations 
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Copyright © 2005 Donald L. Kreider, C. Dwight Lahr, Susan J. Diesel