Question

please help on all! mostly on 32, how can i tell from the directional field?

dN 18) Given the differential equation dt and the initial condition No-5000 determine the limit. 4200 04N (1-N1) A) lim N(t) Does Not Exist Pihn 4200 4 00 B) lim N(t) t-n 04200 O lim N(t)-o t D) lim N(t)-4200 33) Sterile fruit flies are used in an experiment wshere the proportion that survive at least t days is given by e 0.25t The experiment begins with 400 fruit flies, and flies are added at a rate of 10 per hour. Find the expression that you would evaluate to find the number of flies 20 days after the start of the experiment. 20 X.25 25 (20-tdt 20 20 240e -0.25t dt 25 400e to e J A) 400e-5 0 -5.25tdt 10e 20 10e-0.25t dt B) 400e-5 20 10e-0.25(20-t)dt 00c-5 20 240c-0.25(20 t)dt D) 400e-5, 32) The differential equation with the given direction field has 2 and 4 as equilibria. 2 K A) 2 is locally stable and 4 is unstable B) 4 is locally stable and 2 is unstable Cboth are unstable D) both are locally stable 28) The differential equation with the given direction field has 0.5 and 1.5 as equilibria. A) 0.5 is unstable and 1.5 is locally stable B))1.5 is unstable and 0.5 is locally stable C) both are unstable D) both are locally stable 11146///ク

Answer 1

dt 4200 -17 M hoo (4200-N) o.0 4200 dN C4200-N) 4200 + 4200-N 4r00 N ニ 4200-N/ nN-on4r00-N) 00yヒ+C INI 17200-r Ce 6.04E C 0.046 NO000 4200-N So00ニC っしニ-25 -300 C So 4200-5000 So N 6.25e 4200-N 42001625)e 6.2N e 262s 04 N(1+6as) 6-2 N) 2620 eoy 1+6.2rp0.04 2621 6-25 26250 ちho.2 D6.25 G2y

32. Since dineuhin fe io not afbra chiry egniliiG b0 th the euilibvia ane unatakla