Question

A population of insects in a certain region will grow at a rate that is proportional to their current population with proportionality constant k. In the absence of any outside factors the population will triple in two weeks in time. On any given day there is a net migration into the area of 15 insects and 16 are eaten by the local bird population and 7 die of natural causes. If there are initially 100 insects in the area, will the population survive? If not, when do they die out? Make sure to define variables!

Answer 1

As, insccts ill bon af a ratt that is proporHonal to the Ansiwes cuTrent population e YR and, PCrPs)(16 +7) P lo) 100 PCO) 10o -. as, inthe absence fatos outside cquation the = 30 o P4 PCE= CCt AS Ce100 300-100e 300 P (14) = 100 then diuide both side by l00 3 - e n 3- n elu n 3 14r and

-Qu3E aPT ostdt -Se dt - Pe--tn3 +C 14 Lu 3 in 3 12{1q467ie in3 PCE)2 (100-2 n3 In3 doys 0 q4679 e ESt: 50.441S. doy Answ So 4415 Asvive pipadation cuing timt in uhic urap ot Hhe P(t 100 60 4아 20 10 20 30 40 50