s09_mthsc208_hw05

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

Info iconThis preview shows page 1. Sign up to view the full content.

View Full Document Right Arrow Icon
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
Background image of page 1
This is the end of the preview. Sign up to access the rest of the document.

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...
View Full Document

This note was uploaded on 03/12/2012 for the course MTHSC 208 taught by Professor Staufeneger during the Spring '09 term at Clemson.

Ask a homework question - tutors are online