Question

The function D(t) = 5e^-0.4t can be used to find the number of milligrams d, of a certain drug that is in a patient's bloodstream t,hours after the drug has been administered(a) What is the initial amount of drug administered to the patient? Round decimalto two places.(b) Use functional notation toexpress how many milligrams will be present after 1 hour. Then calculate the value.Functional Notation:___Calculated Value:___Round decimal to two places.(c) Determine how many milligrams will bepresent after 8 hours

Answer 1

Given function:

`D(t)=5e^(-0.4t)`

Where D is the number of milligrams of drugs

t is time

(a) The initial amount of drug administered.

The initial amount of drug administered is the drug administered at t = 0

Hence:

`\begin{gathered} D(t=0)\text{ = 5 }* e^(-0.4*0) \\ =\text{ 5 milligrams} \end{gathered}`

(b) The number of milligrams that would be present after 1 hour

Here, we substitute 1 for t into the function:

Functional notation:

`D(t=1)\text{ =5}* e^(-0.4*1)`

Calculated Value:

`D(t=1)\text{ = 3.35 milligrams}`

(c) The number of milligrams present after 8 hours:

`\begin{gathered} D(t=8)\text{ = 5}* e^(-0.4*8) \\ =\text{ 0.20 milligrams} \end{gathered}`