Problem

The following table shows the amount of caffeine in Trey's bloodstream at various times since he drank a cup of coffee.
\begin{tabular}{|c|c|}
\hline \# of hours since he drank the coffee & \# of mg of caffeine in his bloodstream \\
\hline 0 & 300 \\
\hline 1 & 270 \\
\hline 2 & 243 \\
\hline 3.5 & 207.477 \\
\hline 4.5 & 186.7293 \\
\hline
\end{tabular}
a. What is the 1-hour growth (or decay) factor for the number of mg of caffeine in Trey's bloodstream?
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b. What is the 1-hour percent change for the number of mg of caffeine in Trey's bloodstream?
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Answer

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Answer

Final Answer: The 1-hour growth (or decay) factor for the number of mg of caffeine in Trey's bloodstream is \(\boxed{0.9}\).

Steps

Step 1 :The 1-hour growth (or decay) factor for the number of mg of caffeine in Trey's bloodstream can be calculated by dividing the amount of caffeine in his bloodstream after 1 hour by the initial amount of caffeine in his bloodstream.

Step 2 :Let's denote the initial amount of caffeine as \(initial\_caffeine\) and the amount of caffeine after 1 hour as \(caffeine\_after\_1\_hour\).

Step 3 :From the table, we know that \(initial\_caffeine = 300\) and \(caffeine\_after\_1\_hour = 270\).

Step 4 :Then, the 1-hour growth (or decay) factor, denoted as \(growth\_factor\), can be calculated as \(growth\_factor = \frac{caffeine\_after\_1\_hour}{initial\_caffeine} = \frac{270}{300} = 0.9\).

Step 5 :Final Answer: The 1-hour growth (or decay) factor for the number of mg of caffeine in Trey's bloodstream is \(\boxed{0.9}\).

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