Final Answer:
It would take approximately 55 minutes (Option B) for a sample of P-32 to decay from an activity of 10,000 counts per minute to 8,500 counts per minute.
Step-by-step explanation:
The decay of a radioactive substance follows the exponential decay formula: N(t) = N₀e^(-kt), where N(t) is the quantity at time t, N₀ is the initial quantity, k is the decay constant.
The count rate is proportional to the quantity, so C(t) = C₀e^(-kt), where C(t) is the count rate at time t, C₀ is the initial count rate.
Rearrange the formula to solve for t: t = -1/k * ln(C(t)/C₀).
Use the provided count rates (10,000 and 8,500 counts per minute) and solve for t.
The calculated time is approximately 55 minutes, confirming Option B as the correct answer.