Final answer:
The correct decay formula for the given situation is 1,240 × (0.93)^t. After 3 hours, there would be approximately 1,039.13 atoms remaining, and after 3 days, approximately 5.33 atoms, although the actual number must be a whole atom.
Step-by-step explanation:
The correct formula for the decay in this situation should represent the fact that 7% of the radioactive material decays each hour. Therefore, each hour we retain 93% (or 0.93) of the material. Since this decay happens every hour, we raise the decay rate to the power of the number of hours passed. The correct decay formula is therefore 1,240 × (0.93)^t, where 't' is the number of hours.
To find out how many atoms will be in the rock after 3 hours, we replace 't' with 3: 1,240 × (0.93)^3. After calculating this, we find that there will be approximately 1,039.13 atoms left.
Considering there are 24 hours in a day, 3 days will be equivalent to 3 × 24 = 72 hours. To find the number of atoms after 3 days, we use the formula with 't' replaced by 72, which gives us 1,240 × (0.93)^72. This calculation yields approximately 5.33 atoms.
Since we cannot have a fraction of an atom, we would expect that there would be either 5 or 6 atoms left, depending on the rounding strategy in context.