Question

The concentration of a drug in the body fluids is given by C = Coe-0.81, where Co is the initial dosage and t is the time in hours elapsed after administering the dose.85 mg of a drug is given, how much time elapses until 21 mg of the drug remains? Round your answer to two decimal places, if necessary._____ hours

Answer 1

Given

The equation is given as

`C=C_oe^(-0.8t)`

here C is the remaining dosage and Co is the initial dosage.

Step-by-step explanation

To find the time elapses until 21 mg of the drug remains.

`\begin{gathered} 21=85e^(-0.8t) \\ 0.2470588=e^(-0.8t) \end{gathered}`

Take ln both sides.

`\begin{gathered} ln\text{ 0.2470588=-0.8tlne} \\ -1.3981289=-0.8t \\ t=(1.3981289)/(0.8) \\ t=1.747hrs \end{gathered}`

Answer

Hence the time elapses until 21 mg of the drug remains is 1.747 hours.