A rare crystal is used in an experiment and starts with a weight of 5 grams. Every 3 hours, the crystal grows by 20% of its current weight. What will be the weight of the crystal in grams after 15 hours?

Sure, let's solve this step by step.

1. Initial weight of the crystal: 5 grams.

2. Growth rate: Every 3 hours, the crystal grows by 20% of its current weight.

3. Total time: 15 hours.

4. Number of growth periods: Since the crystal grows every 3 hours, we need to determine how many 3-hour periods are in 15 hours. $\text{Number of periods} = \frac{15 \text{ hours}}{3 \text{ hours/period}} = 5 \text{ periods}$

5. Weight calculation after each period:

   • Initial weight: 5 grams.
   • After 1st period (3 hours): $\text{New weight} = 5 \text{ grams} \times (1 + 0.20) = 5 \text{ grams} \times 1.20 = 6 \text{ grams}$
   • After 2nd period (6 hours): $\text{New weight} = 6 \text{ grams} \times 1.20 = 7.2 \text{ grams}$
   • After 3rd period (9 hours): $\text{New weight} = 7.2 \text{ grams} \times 1.20 = 8.64 \text{ grams}$
   • After 4th period (12 hours): $\text{New weight} = 8.64 \text{ grams} \times 1.20 = 10.368 \text{ grams}$
   • After 5th period (15 hours): $\text{New weight} = 10.368 \text{ grams} \times 1.20 = 12.4416 \text{ grams}$

6. Final weight of the crystal after 15 hours: 12.4416 grams.

So, the weight of the crystal after 15 hours will be approximately 12.44 grams.