Progress: Element X decays radioactively with a half life of 5 minutes. If there are 520 grams of
Element X, how long, to the nearest tenth of a minute, would it take the element to
decay to 92 grams?
y = a(.5)

9514 1404 393

  2.5 minutes

Step-by-step explanation:

The amount remaining (y) in grams is given by the exponential function ...

  y = 520(.5^t)

We want to find t when y = 92.

  92 = 520(0.5^t)

  92/520 = 0.5^t

  log(92/520) = t·log(0.5)

  t = log(92/520)/log(0.5) ≈ 2.499 ≈ 2.5

It would take 2.5 minutes for the 520 gram sample to decay to 92 grams.

3x1

Step-by-step explanation: