Question

③ The rate of drange in #of skittles is directly proportional to 70 -s(t). T is time in years. to the population is 35 t=2 then population is to t = 3 then population is ? @ 4:00am toong painkiller daily 30% drug stays in body after a aday and top excreted What amount of painkiller is in patients body late 3:59am, immediately before the days dose & giren) after I day and after 2 days of treatment? use geometric series to compute the amount of painkiner in the body after a long time of treatment (at 3:59am immentiately before the days dose is given)

Answer 1

Criven that rate of change in population of Skittles ů directly proportional to 70-5lt t is time in years Criven then population is 35 t=2 thena population is so have to find population when t=3 we Given dsit) & 70-14) at ds(t) = K[70-$(t)) dt Where ů proportionality constant ds(t) Kdt 70-SLU) integrate both sides ds 70-s f Kat. firs= (lt)} - ln(70-5) = ktte en/70-12 Kt-c move in to - other side 70-S = -Kt-c е, ékt e-c 70-S = ekt A & AB = KAKO {:: AS · CH Both gepresent constant -kt 70-e A = S kt slt)= 70 de

So at population is t=3 then 64.655 Š 65