The rate at which the concentration of a drug in the bloodstream decreases is proportional to the concentration at any time t. Initially, the concentration of the drug in the bloodstream is C0 g/mL. What is the concentration of the drug in the bloodstream any time t

Explanation:

From the given information:

At any given time (t), let c(t) represent the concentration of the drug present in bloodstream.

Deriving the equation:

decrease proportionally to Concentration C

i.e

㏑(C) = -kt + λ

where,

λ is the integration constant.

Integrating at t = 0, concentration of blood = Co g/mL

C(0) = Co

㏑(C₀) = 0 + λ

λ = ㏑(C₀)

From ㏑(C) = -kt + λ

㏑(C) = -kt + ㏑C₀

㏑(C)  - ㏑C₀ =  -kt

∴

The concentration of drug in blood at any time t is: