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A rock of radioactive material decays at a rate of 7% an hour. There are currently 1,240 atoms in the rock. What would the formula for decay look for in this situation? How many atoms will be in the rock after 3 hours? How many atoms will be in the rock after 3 days?

a. Decay formula:1,240×(0.93)^t; After 3 hours: __ atoms; After 3 days: __ atoms
b. Decay formula:1,240×(1.07)^t; After 3 hours: __ atoms; After 3 days: __ atoms
c. Decay formula:1,240×(0.93)^3t; After 3 hours: __ atoms; After 3 days: __ atoms
d. Decay formula:1,240×(1.07)^3t; After 3 hours: __ atoms; After 3 days: __ atoms

1 Answer

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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.

User Daniel Rearden
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