Element X decays radioactively with a half life of 9 minutes. If there are 720 grams of Element X, how long, to the nearest tenth of a minute, would it take the element to decay to 255 grams?

You start with 720 grams of element X, which has a half life of 9 minutes. How much time will it take until only 255 grams remain?

elapsed time = half life * log (beginning amount / ending amount) / log 2

elapsed time = 9 * log (720 / 255) / log (2)

elapsed time = 9 * log (2.8235294118 ) / log (2)

elapsed time = 9 * 0.450792316 / 0.30102999566

elapsed time = 9 * 1.4974996595

elapsed time = 13.4774969355  minutes

Since the problem wants this rounded to the nearest tenth of a minute:

elapsed time = 13.5 minutes

Step-by-step explanation:

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