CONCENTRATION of A Drug in an Organ A drug is carried into an organ of volume V cm 3 by a liquid that enters the organ at the rate of a cm /sec and leaves it at the rate of b cm /sec. The concentration of the drug in the liquid entering the organ is b g/cm. If the concentration of the drug in the organ at time t (in seconds) is increasing at the rate of x ′ ( t ) = 1 V ( ac − b x 0 ) e − bt1V g/cm 3 /sec and the concentration of the drug in the organ initially is x 0 g/cm 3 , show that the concentration of the drug in the organ at time t is given by x ( t ) = ac b ( x 0 − ac b ) e − bt1V
CONCENTRATION of A Drug in an Organ A drug is carried into an organ of volume V cm 3 by a liquid that enters the organ at the rate of a cm /sec and leaves it at the rate of b cm /sec. The concentration of the drug in the liquid entering the organ is b g/cm. If the concentration of the drug in the organ at time t (in seconds) is increasing at the rate of x ′ ( t ) = 1 V ( ac − b x 0 ) e − bt1V g/cm 3 /sec and the concentration of the drug in the organ initially is x 0 g/cm 3 , show that the concentration of the drug in the organ at time t is given by x ( t ) = ac b ( x 0 − ac b ) e − bt1V
Solution Summary: The author explains the expression for the rate of change of concentration of the drug in the organ at time t.
CONCENTRATION of A Drug in an Organ A drug is carried into an organ of volume V cm3 by a liquid that enters the organ at the rate of a cm /sec and leaves it at the rate of b cm /sec. The concentration of the drug in the liquid entering the organ is b g/cm. If the concentration of the drug in the organ at time t (in seconds) is increasing at the rate of
x
′
(
t
)
=
1
V
(
ac
−
b
x
0
)
e
−
bt1V
g/cm3/sec and the concentration of the drug in the organ initially is x0 g/cm3, show that the concentration of the drug in the organ at time t is given by
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