To complete the table showing the amount of the drug in your blood over time, we'll follow these steps:
1. Initial Amount: You start with 1000 milligrams of the drug.
2. Filtration Rate: The kidneys filter out 25% of the drug every 4 hours.
3. Calculation:
- After 4 hours, 25% of the original 1000 mg is filtered out, which means 75% remains:
[tex]\[
1000 \times 0.75 = 750 \text{ mg}
\][/tex]
- After another 4 hours (8 hours total), 25% of the remaining 750 mg is filtered out, so 75% remains:
[tex]\[
750 \times 0.75 = 562 \text{ mg (approx)}
\][/tex]
- This process continues, multiplying the remaining amount by 0.75 every 4 hours.
Following this procedure, we calculate the remaining amounts for each 4-hour interval up to 68 hours. Here are the detailed values:
[tex]\[
\begin{array}{|c|c|}
\hline
\text{TIME SINCE TAKING (HR)} & \text{AMOUNT OF DRUG (MG)} \\
\hline
0 & 1000 \\
\hline
4 & 750 \\
\hline
8 & 562 \\
\hline
12 & 422 \\
\hline
16 & 316 \\
\hline
20 & 237 \\
\hline
24 & 178 \\
\hline
28 & 134 \\
\hline
32 & 100 \\
\hline
36 & 75 \\
\hline
40 & 56 \\
\hline
44 & 42 \\
\hline
48 & 32 \\
\hline
52 & 24 \\
\hline
56 & 18 \\
\hline
60 & 14 \\
\hline
64 & 10 \\
\hline
68 & 8 \\
\hline
\end{array}
\][/tex]
So, the completed table would look like this:
\[
\begin{array}{|c|c|}
\hline \begin{tabular}{l}
TIME SINCE TAKING \\
THE DRUG (HR)
\end{tabular} & \begin{tabular}{l}
AMOUNT OF DRUG \\
IN YOUR BLOOD (MG)
\end{tabular} \\
\hline 0 & 1000 \\
\hline 4 & 750 \\
\hline 8 & 562 \\
\hline 12 & 422 \\
\hline 16 & 316 \\
\hline 20 & 237 \\
\hline 24 & 178 \\
\hline 28 & 134 \\
\hline 32 & 100 \\
\hline 36 & 75 \\
\hline 40 & 56 \\
\hline 44 & 42 \\
\hline 48 & 32 \\
\hline 52 & 24 \\
\hline 56 & 18 \\
\hline 60 & 14 \\
\hline 64 & 10 \\
\hline 68 & 8 \\
\hline
\end{array}
