Final answer:
The initial amount of Fluorine-18 administered to the patient was 160 grams.
Step-by-step explanation:
To solve this problem, we can use the formula for radioactive decay. The formula is: final amount = initial amount × (1/2)^(number of half-lives). In this case, the half-life of Fluorine-18 is 2 hours, which is equivalent to 120 minutes. Since the patient still has 20 grams remaining after 360 minutes, we can calculate the number of half-lives it took to reach that point. 360 minutes / 120 minutes per half-life = 3 half-lives. Plugging this into the formula, we get: 20 grams = initial amount × (1/2)^3. Solving for the initial amount, we find: initial amount = 20 grams × 2^3 = 160 grams.