SOLUTION
We want to calculate the amount of drug remaining in the blood stream at any given time
To do this we are told to use the formula
[tex]\begin{gathered} A(t)=A_0e^{-0.316t} \\ \text{Where } \\ A(t)\text{ = amount of drug remaining } \\ A_0=\text{ initial amount of drug taken = 550 mg} \\ t=\text{ time in hours } \end{gathered}[/tex]
So, to get each we substitute the values 550 and each value of time t into the equation.
For t = 0 hours we have
[tex]\begin{gathered} A(t)=A_0e^{-0.316t} \\ A(0)=550_{}e^{-0.316\times0} \\ =550e^0 \\ e^0=1 \\ =550\times1=550 \end{gathered}[/tex]
Hence for t = 0, the answer is 550.000 to the nearest thousandth
Now for t = 1 hour, we have
[tex]\begin{gathered} A(t)=A_0e^{-0.316t} \\ A(1)=550_{}e^{-0.316\times1} \\ A(1)=550_{}e^{-0.316} \\ =400.982697 \end{gathered}[/tex]
Hence for t = 1 hour the answer is 400.983 to the nearest thousandth
Now, let us run this using the excel sheet
Now, we input the time(s) and the formula into the excel sheet, we have
After imputing the formula, next we set it to 3 decimal places, then we click and run
After doing this, here is the final answer to your question
