9)The spread of a virus is modeled by the function: V(t)= -t^2 + 6t - 4 where V(
ID: 2876698 • Letter: 9
Question
9)The spread of a virus is modeled by the function: V(t)= -t^2 + 6t - 4 where V(t) is the number of people (in hundreds) with he virus and t is the number of weeks since the first case was observed.
A) What is a reasonable domain for this problem?
B) When does the number of cases reach a maximum?
C) What is the maximum number of cases?
D) Find the rate of change function (or V' (t))
E) What is the rate of change in the number of cases at the maximum?
F) Give the sign (+ or -) of the rate of change up to the maximum and after the maximum.
Up to the maximum: After the maximum:
Explanation / Answer
given V(t)= -t^2 + 6t - 4
A) number of people always greater than 0
-t^2 + 6t - 4 >0
=>t^2 -6t +4<0
3-5 < t<3+5
reasonable domain =(3-5 ,3+5)
B) number of cases reach a maximum at mid point of interval
t =[3-5 +3+5]/2
t =3
C)maximum number of cases =V(3)=-3^2 + 6*3 - 4
maximum number of cases=-9+18-4
maximum number of cases=5 hundred
D) rate of change functionV'(t)=-2t +6
E) rate of change in the number of cases at the maximum , t=3
V'(3)=-2*3 +6
V'(3)=0
F) the sign of the rate of change
Up to the maximum: + After the maximum: -
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