s09_mthsc208_hw05

# s09_mthsc208_hw05 - 9 per year a What is the logistic...

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MTHSC 208, HW 5 (1) Section 2.5: # 6, 7, 9, 11-13. (2) Section 2.9: # 16, 20, 22. (3) Sketch a slope ﬁeld for the equation y 0 = y (1 - y ) and use this to sketch several solution curves. (4) On the same diagram, sketch the solutions to y 0 = y (1 - y ) and y 0 = 0 . 3 y (1 - y ) both satisfying the initial condition y (0) = 0 . 5. Explain how the diﬀerence in the equation explains the diﬀerence in these two curves. (5) Let y 0 = ky (1 - y 10 ) and y 0 (0) = 2 and y (0) = 5. a. What is k ? Hint: No need to solve for y ( t ) yet! b. What is y (3)? (6) The population of a certain planet is believed to be growing according to the logistic equa- tion. The maximum population the planet can hold is 10 10 . In year zero the population is 50% of this maximum, and the rate of increase of the population is 10
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Unformatted text preview: 9 per year. a. What is the logistic equation satisﬁed by the population, P ( t )? b. How many years until the population reaches 90% of the maximum? (7) A colony of bacteria is growing in a petri dish which has a maximum capacity of 100 mg. The mass of bacteria is increasing at a rate given by the logistic equation. Initially there is 2 mg of bacteria and the rate of increase is 1 mg per day. a. Write down the logistic equation satisﬁed by the mass, M ( t ). b. When will the mass of bacteria be 50 mg? c. What is the mass of bacteria 10 days after the mass was 2mg? 1...
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## This note was uploaded on 03/12/2012 for the course MTHSC 208 taught by Professor Staufeneger during the Spring '09 term at Clemson.

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