Chapter 5.4, Problem 59PE

(a)

To determine

To calculate: The equation for the model $A\left(t\right)=A_0{e}^{-kt}$, where the initial concentration of the drug in blood is represented by $A_0$.

(b)

To determine

To calculate: The equation for the model $A\left(t\right)=A_0{e}^{-kt}$ for $A\left(t\right)=0.655,t=4$.

(c)

To determine

To calculate: The value of $k$ for the equation $0.69=A_0{e}^{-3k}$, $0.655=A_0{e}^{-4k}$ (rounded to $3$ decimal places).

(d)

To determine

To calculate: The initial concentration $A_0$ in $\left(\mu g/dL\right)$ at time of injection (rounded to $2$ decimal places) if the equation is $0.69=A_0{e}^{-3k}$,$k=0.052$.

(e)

To determine

To calculate: The concentration of drug after $12$ hours (rounded to $2$ decimal places) for the model $A\left(t\right)=A_0{e}^{-kt}$ represents the drug concentration $A\left(t\right)$ in $\left(\mu g/dL\right)$$t$ hours after injection,$A_0\approx 0.81\mu g/dL$,$k\approx 0.052$.