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That is completely unrealistic. C-14 has a half-life of several thousand years, not a few hours as implied in this example.

Anyway, to solve this in general you can write the exponential equation:

N = N0e-λt

where N is the remaining amount, N0 is the original amount, λ is the decay constant, and t is the time. Replace the numbers you know, and solve for λ. Note that the "disintegrations per minute" are proportional to the amount of remaining substance, so you can just as well assume that those numbers represent the remaining amount.

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