Question

The number of milligrams Dh of a drug in a patient's bloodstream h hours after the drug is injected is modeled by the following function.=Dh5e−0.45hFind the initial amount injected and the amount in the bloodstream after 8 hours. Round your answers to the nearest hundredth as necessary.

Answer 1

Recall that to evaluate a function at a given value, we substitute the variable with the given value.

Since h represents the number of hours after the drug is injected, then the initial amount of drug is at h=0. Evaluating D(h) at h=0 we get:

`D(0)=5e^(-0.45*0)=5e^0=5.`

Therefore the initial amount of drug in the blood is 5 milligrams.

Evaluating D(h) at h=8 we get:

`\begin{gathered} D(8)=5e^(-0.45*8)=5e^(-3.6) \\ \approx0.14. \end{gathered}`

Answer:

`\begin{gathered} Initial\text{ }amount:\text{ }5milligrams. \\ Amount\text{ }after\text{ }8\text{ }hours:\text{ }0.14milligrams. \end{gathered}`