6.2 Growth and Decay Obj: set up and solve growth and decay problems.

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Presentation transcript:

6.2 Growth and Decay Obj: set up and solve growth and decay problems

Review of Growth and Decay Model  Compound Interest Formula  Continuously Compounding Interest Formula

As a Differential Equation…

Example  Suppose 10 g of Pu-239 was released in the Chernobyl nuclear accident. How long will it take for 10 g to decay to 1 g?Pu-239  Pu-239 has a half life of 24,100 years  80,059 years!

Variation  Direct Variation  Inverse Variation  Joint Variation

Example  Model: the rate of change of P with respect to t is proportional to 10 – t.

Practice  The number of bacteria in a culture is increasing according to exponential growth. There are 125 after 2 hours and 350 after 4 hours.  1. Find the initial population.  2. Write a model to show the growth after t hours.  3. Use the model to find the number after 8 hours.  4. After how many hours will the number of bacteria be 25000?

Assignment  Assignment: Page 400 1, 3, 15, 17, 21, 33, 39, 45, 51, 57