Question

The logistio equation for the population in thousanda) of a certain species is given by - 3702 -20°. Completo parts (a) through (m) below. (a) Sketch the direction field by using either a computer software package or the method of soclines. Choose the correct sketch below. ОА AP OC Pop out (b) If the initial population is 2000 (that is, p10) -2]what can be said about the limiting population im pit? If p(0) = 2, then lim pr)- ). The population wit

Answer 1

2 / X -2 2 A(2, -1) -1

(a) de field in drawn on dt (2) A = (2x-3) o -1 = ㅋ 3p2-253 -(1) direction follows: Am: (B) (b) dok = 3p2-2p3 , Blo) = 2 dhe p² (3p-2 Þ) db Þ? (3-25) Comider 1 B ( By partial ba (3-2) Þ2 (20-3) fraction) b2c +Þ(25-3) A+(2p-3)B 52 (25-3) p2 (2-3) -1 = bac + Þ(25-3) A+ (2-3) 3 - -1 = 52 (2A+C) +pl-3 A+ 2B) - 3B so 2A +C =0 > A = 2 , B = 423 , (= -4/5 - 3A +2B=0 - 313 = -1 4 ар dt ор 353 integrating both sides, we get In p 2 ln 12 p-3) =t+ c -(3) - Őb Now plo)=2 > 2 lna 1 2 In 1 = 9 6 → . 1 so (2) » 2 t 9(2þ-3) ģ g 9 2 lna - ļ - 2 dna ñ 1 Cla 0.01 3 ho 2 ln p- 2 ln (2 p-3) =t-0.013 g 3b g I t-0.013 In p²19 CScanned with amScanne2b-3)219 3 b 11

( 23 ) - 9 en > In (26-2) "'°C és pon ) = +-0.013 219 1181) t-0.013 In / P en e 2 D-3 219 to 0.013 р It-0.013) e t +0.013) -1|(36) Р 219 2 p-3 1 (31) 219 > e Now as to Rinis = e 11(3b) so 2 p-3 e tto.013 o (2 =( (² p. +0 herer o D no 219 2 p-3 2 þ-3 = 0 pa rollin CScanned with teamScanner tan plt) = 3 २