Question

Certain drugs are eliminated from the bloodstream at an exponential rate. Doctors and pharmacists need to know how long it takes for a drug to reach a certain level to determine how often patients should take medications. Answer the following questions about this situation.A. Select the correct statement:_The same amount of the drug will be eliminated in the first hour as in the second hour._Less of the drug will be eliminated in the first hour than in the second hour._More of the drug will be eliminated in the first hour than in the second hour.B. Write an exponential equation for the following situation. The drug dosage is 500 mg. The drug is eliminated at a rate of 5.2% per hour. Use D = the amount of the drug in milligrams and t = time in hours_______C. How much of the drug is left after 6 hours? Round to the nearest milligram._______Milligram

Answer 1

Item b.)

To solve that item we must remember the general formula for exponential decay, it's

`f(t)=A(1-r)^t`

Then, let's modify it to fit our parameters

A is the initial value, in our case, the initial value is the dosage, 500mg, then A = 500

r is the rate, we have 5.2%, then the value of r will be 0.052

And f(t) will transform into D, changing the name.

Hence

`D=500(1-0.052)^t`

We can also simplify the subtraction, we get

`D=500\cdot(0.948)^t`

Item c.)

To solve that we will use our equation, we will input t = 6 hours and find the value of D.

`\begin{gathered} \begin{equation*} D=500\cdot(0.948)^t \end{equation*} \\ \\ D=500\cdot(0.948)^6 \\ \\ D=500\cdot0.726 \\ \\ D=363\text{ mg} \end{gathered}`

The answer is 363 mg