Question

Certain drugs are eliminated from the bloodstream at an exponential rate (for example, 10% of a drug eliminatesfrom the blood per hour). Write an exponential model for the following situation. The drug dosage is 600 mg, Thedrug is eliminated at a rate of 5.3% per hour. Use D as the amount of the drug in milligrams and t as the time inhours.D=________ (type an expression using t as the variable.)How much of the drug is left after 4 hours?

Answer 1

Step-by-step explanation:

If the dug dosage is 600 mg and 5.3% is eliminated per hour, we have:

`\begin{gathered} D(t)=600\cdot(1-(5.3)/(100))^t \\ D(t)=600\cdot((94.7)/(100))^t \\ D(t)=600\cdot(0.947)^t \end{gathered}`

Because for each hour the drug is eliminated at a rate of 5.3%, so the 94.7% of the previous amount remains.

Answer:

`D(t)=600\cdot(0.947)^t`

How much of the drug is left after 4 hours?

`\begin{gathered} D(4)=600\cdot(0.947)^4 \\ D(4)\approx4.82.5598\text{ mg} \\ \end{gathered}`