A drug is carried into an organ of volume by a liquid that enters the organ at the rate of and leaves it at the rate of .The concentration of the drug in the liquid entering the organ is .If the concentration of the drug in the organ at time is increasing at the rate of , and the concentration of the drug in the organ initially is , find the concentration of the drug in the organ at time .

Question

A drug is carried into an organ of volume   by a liquid that enters the organ at the rate of  and leaves it at the rate of  .The concentration of the drug in the liquid entering the organ is  .If the concentration of the drug in the organ at time  is increasing at the rate of   , and the concentration of the drug in the organ initially is  , find the concentration of the drug in the organ at time  .

Quizplus · Accepted Answer

We can use the formula:

dC/dt = (C₀Fᵢ - CᵢF + R)/V

where:
dC/dt = rate of change of concentration of drug in the organ
C₀ = initial concentration of drug in the liquid entering the organ
Fᵢ = rate of flow of liquid entering the organ
Cᵢ = concentration of drug in the liquid leaving the organ
F = rate of flow of liquid leaving the organ
R = rate of drug entering the organ due to other sources
V = volume of the organ

Substituting the given values, we get:

11eb12b0_a989_b440_b394_0ff2457dff33_TB7866_11 = (11eb12b0_a989_db52_b394_21f1b696fe84_TB7866_11 * 11eb12b0_a989_b43c_b394_9b5cf7f928a8_TB7866_11 - 11eb12b0_a989_b43e_b394_ffcf4a4092e9_TB7866_11 * 11eb12b0_a989_b43d_b394_8733dfc2a1a6_TB7866_11 + R)/11eb12b0_a989_8d2a_b394_6ba2674b6389_TB7866_11

Simplifying the equation, we get:

R = 11eb12b0_a989_0268_b394_de0556f620b2_TB7866_11

Substituting the value of R into the above equation and integrating, we get:

C = 11eb12b0_a98a_0267_b394_f92b5d607611_TB7866_11

Therefore, the concentration of the drug in the organ at time 11eb12b0_a989_db53_b394_3d696033befb_TB7866_11 is 11eb12b0_a98a_0267_b394_f92b5d607611_TB7866_11, which is choice D.

A Drug Is Carried into an Organ of Volume