Problem

b. The expression $225 \cdot\left(\frac{1}{2}\right)^{\frac{1}{2}}$ represents the amount of medicine in the body some time after it is administered. What is that time?

Answer

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Answer

\(\boxed{0.5}\) hours (30 minutes) after it is administered.

Steps

Step 1 ：Let \(A(t) = 225 \cdot\left(\frac{1}{2}\right)^t\) represent the amount of medicine in the body at time \(t\) hours after it is administered.

Step 2 ：We want to find the time \(t\) when \(A(t) = 225 \cdot\left(\frac{1}{2}\right)^{\frac{1}{2}}\).

Step 3 ：Set up the equation: \(225 \cdot\left(\frac{1}{2}\right)^t = 225 \cdot\left(\frac{1}{2}\right)^{\frac{1}{2}}\)

Step 4 ：Solve for \(t\): \(t = \frac{1}{2}\)

Step 5 ：\(\boxed{0.5}\) hours (30 minutes) after it is administered.

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