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
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.
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