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The problem provided deals with nuclear medicine, specifically the decay of the radioactive isotope Fluor-18, which is used in cancer treatment. The table shows the decay of Fluor-18 over time, and the task is to determine whether by the end of the day (presumably 24 hours), there will be any remaining trace of Fluor-18 in the sample.

### Data from the table:
- **0 hours:** 380 MBq
- **1 hour:** 266 MBq
- **2 hours:** 186.2 MBq
- **3 hours:** 130.34 MBq
- **4 hours:** 91.238 MBq
- **5 hours:** 63.8666 MBq

This represents an exponential decay process, where the quantity of Fluor-18 decreases exponentially with time.

### Exponential Decay Model:
The general formula for radioactive decay is:
\[
Q(t) = Q_0 \cdot e^{-kt}
\]
Where:
- \( Q(t) \) is the quantity of substance at time \( t \),
- \( Q_0 \) is the initial quantity (380 MBq at \( t = 0 \)),
- \( k \) is the decay constant,
- \( t \) is the time in hours.

To solve the problem algebraically, we can fit this model to the data and then predict the remaining quantity after 24 hours. Let's start by determining the decay constant \( k \) from the given data, then use it to find the quantity remaining at the end of the day.

Let me calculate the decay constant and the remaining quantity after 24 hours.The exponential decay model yields the following results:

- Initial quantity \( Q_0 = 380 \) MBq (as expected from the data).
- Decay constant \( k = 0.357 \, \text{per hour} \).

Using this model, the quantity of Fluor-18 remaining after 24 hours is approximately:
\[
Q(24) \approx 0.073 \, \text{MBq}.
\]

Thus, while most of the Fluor-18 will have decayed by the end of the day, there will still be a very small trace remaining (about 0.073 MBq).

Would you like more details or further explanation on this? 

Here are some follow-up questions to explore:

1. What is the half-life of Fluor-18 based on this decay constant?
2. How long will it take for the Fluor-18 to reach a level of less than 1 MBq?
3. How would this model change if the decay constant were different?
4. Could external factors affect the decay rate of Fluor-18?
5. What is the biological impact of small remaining traces of Fluor-18 after 24 hours?

**Tip:** Understanding the decay constant \( k \) is key to predicting how long it takes for a substance to decay significantly.

En médecine nucléaire, on utilise certaines substances radioactives qu’on appelle les isotopes radioactifs à des fins thérapeutiques. Le radio-isotope Fluor-18 est par exemple utilisé en tant que traceur en cancérologie. Ces radio-isotopes ont comme particularité de se désintégrer une fois administrés au patient après une certaine période. Une équipe d’étudiants en médecine nucléaire observent l’évolution du Fluor-18 dans un échantillon en mesurant la quantité restante au cours du temps. Les résultats sont regroupés dans le tableau ci-dessous : Nombre de périodes passées (en heures), Quantité restante du Fluor-18 dans l’échantillon (MBq). En analysant ces résultats, est-ce qu’on peut affirmer qu’à la fin de la journée il ne restera aucune trace du Fluor-18 dans l’échantillon? Une démarche algébrique est demandée.

This problem involves the exponential decay of the Fluor-18 isotope used in nuclear medicine. Using the formula Q(t) = Q_0 * e^(-kt), students are asked to determine the remaining quantity of Fluor-18 at the end of a 24-hour period. The problem is suitable for high school students in Grades 10-12.

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