..ooo AT&T; 12:35 PM 100% 48. The gamn 0 0 da 0 43. The rate, r, at which people
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..ooo AT&T; 12:35 PM 100% 48. The gamn 0 0 da 0 43. The rate, r, at which people get sick during an epidemic of the flu can be approximated by r 1000te-0.51 where r is measured in people/day and t is measured in days since the start of the epidemic (a) Find (b) Integ positi (a) Sketch a graph of r as a function of t. (b) When are people getting sick fastest? (c) How many people get sick altogether? (c) Find gers Strengthen Your Understanding In Problems 49-50, explain what is wrong with the statement. false. Give an 49. If bothJ) d and g) d diverge, then so 53. If f is co does J f(n)g(a)dz. 50. Ifj" f(x) dx diverges, then lin,s/(x)0 then so do 50. If J. f(z) dx diverges, then limx,f(z) 54. If f(x) is diverges In Problems 51-52, iye anexampl In Problems 51-52, give an example ofExplanation / Answer
43
b)
r =1000t e-0.5t
people get sick fastest when dr/dt =0
dr/dt =1000(1 e-0.5t+t(-0.5)e-0.5t)
dr/dt =1000(1-0.5t)e-0.5t=0
1-0.5t =0
t =1/0.5
t =2
when t<2, dr/dt >0 , t>2, dr/dt <0, so people get sick fastest when t =2days
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c)r =1000t e-0.5t
total number of people that get sick = [0 to ]1000t e-0.5tdt
u =1000t , dv =e-0.5tdt ,v =(-1/0.5)e-0.5t=-2e-0.5t, du =1000dt
u dv =uv -vdu
total number of people that get sick = [0 to ]1000t*(-2e-0.5t) - [0 to ]-2e-0.5t*1000dt
total number of people that get sick = [0 to ](-2000te-0.5t) + [0 to ](2000/-0.5)e-0.5t
total number of people that get sick = [0 to ](-2000te-0.5t) - [0 to ](4000)e-0.5t
total number of people that get sick = limt->(-2000te-0.5t) -limt->0(-2000te-0.5t) - ((4000)e--(4000)e0)
total number of people that get sick =0 -0 - (0-(4000))
total number of people that get sick = 4000
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