Asked by Remy
The concentration C of a chemical in the bloodstream 't' hours after injection into muscle tissue is given by:
C=(3t^2+t)/(t^3+50) where t≥0
What is the rate of change over the interval [0,4]? What is the rate of change over the interval [4,8]? What is the horizontal asymptote of the function? Interpret the meaning of this data in the context of the problem.
C=(3t^2+t)/(t^3+50) where t≥0
What is the rate of change over the interval [0,4]? What is the rate of change over the interval [4,8]? What is the horizontal asymptote of the function? Interpret the meaning of this data in the context of the problem.
Answers
Answered by
Reiny
Since you want the rate of change over an interval, it is not "instantaneous" change, so we don't have to use Calculus.
C(0) = 0/50 = 0
C(4) = 52/114
rate of change for [0,4]
= (52/114 - 0)/(4-0) = 13/114
do the same for [4,8]
as t ---> ∞
C ---> 3 , the horizontal asymptote
It suggest that the concentration approaches and remains 3 units, which seems unreasonable
C(0) = 0/50 = 0
C(4) = 52/114
rate of change for [0,4]
= (52/114 - 0)/(4-0) = 13/114
do the same for [4,8]
as t ---> ∞
C ---> 3 , the horizontal asymptote
It suggest that the concentration approaches and remains 3 units, which seems unreasonable
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