341h3 - M341 H3 (S. Zhang) . 1. EP 2.1: 11, 12, 22, 28...

Info iconThis preview shows pages 1–2. Sign up to view the full content.

View Full Document Right Arrow Icon

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: M341 H3 (S. Zhang) . 1. EP 2.1: 11, 12, 22, 28 (Population Models) ans: 2. Suppose that when a certain lake is stocked with fish, the birth and death rates and are both inversely propor- tional to P . Show that P ( t ) = 1 2 kt + p P 2 If P = 100 and after 6 months, there are 169 fish in the lake, how many will there be after 1 year? ans: Let k = ( - ) / P . d dt P = k 1 P P Z 1 P dP = kdt P ( t ) = 1 2 kt + p P 2 P (0) = 100, P (6) = 169, then k = 1, and P (12) = ( t 2 + 10) 2 = 256 3. The time rate of change of an alligator population P in a swamp is proportional to the square of P . The swamp contianed a dozen alligators in 1988, two dozen in 1998. When will tehre be four dozen alligators in the swamp? What happens there after? ans: P = kP 2 ,- 1 P = kt- C P = 1 C- kt P (0) = 12 , C = 1 12 , P = 12 1- 12 kt P (10) = 24 , k = 1 240 , P = 240 20- t P = 48 , t = 15 t 20 , P 4. Suppose that at time t = 0, half of a logistic population of 100,000 persons have heard a certain rumor, and that the number of those who have heard it is then increasing at the rate of 1000 persons per day. How long will it take for this rumor to spread to 80% of the popuplation? ans: Let the population unit be 1000. M = 100. P = kP ( M- P ) P (0) = 1 and P (0) = 50 1 = k 50(100- 50) , k = 0 . 0004 P = kP ( M- P ) P = MP P + ( M- P ) e- kMt When 80% reached, 80 = 100 50 50 + (100- 50) e- . 04 t t = 34 . 66....
View Full Document

This note was uploaded on 04/07/2008 for the course MATH 341 taught by Professor Zhang during the Fall '08 term at University of Delaware.

Page1 / 3

341h3 - M341 H3 (S. Zhang) . 1. EP 2.1: 11, 12, 22, 28...

This preview shows document pages 1 - 2. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online