Question

(1 point) The population of Cook island has always been modeled by a logistic equation P' =r(C - P) with growth rate r = 2 and carrying capacity C = 6500 with time t in years. Starting in 2000, 8 citizens of Cook Island have left every year to become a mathematician, never to return. What is the new differential equation modeling the population of the island P? 4500 = 0

Answer 1

Answer Page No 0 The population of cook island has been modeled by a logistic equation pls or{c-P) noith. growth rate , va a Carrying capacily, C - 6500 pe o CC-P) 0(C-P) » ven codt Enstegovale on both sides Sop - Sordo -1(C-P) = 076+ c, [where G, integrating concha in (e-P)--(ont + c) C-P = efet +c) Pac-e-(it +co) .: Population ; P = c e Cost + C)

Page No @ Starting in 2000, 8 citizens of coola Poland have left every year to become a mathematician, never to return .:Population, P. c- e-Cort 4c;)- 86 differentiating the above equation dp -1-se-Cat + c)] - 6 ove(et +ci) 5 But , (C-P)= e Cont+C) dP - 01 CC-P) - 8 dt. 0932Ę C = 6500 .:. P = 0 (6500 --P)- dt :: P = 13000 – 2P -8. - 12992 – 28 1 op dp - 12992 – 2p cohere t = 2000 dt. This is the new modeling equation.