Answer:
[tex]C(t) = C_oe^{-kt}[/tex]
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:
[tex]\dfrac{dC}{dt}[/tex] decrease proportionally to Concentration C
i.e
[tex]\dfrac{dc}{dt} \alpha - C[/tex]
[tex]\dfrac{dc}{dt} = -k C[/tex]
[tex]\dfrac{dc}{c} = -k dt[/tex]
[tex]\int \dfrac{dc}{c} = -k \int dt[/tex]
㏑(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
[tex]\dfrac{C}{C_o} = e^{-kt}[/tex]
[tex]C(t) = C_oe^{-kt}[/tex]
∴
The concentration of drug in blood at any time t is:
[tex]C(t) = C_oe^{-kt}[/tex]
