Element X decays radioactively with a half life of 11 minutes. If there are 670 grams of Element X, how long, to the nearest tenth of a minute, would it take the element to decay to 26 grams?

It would take 51.5 minutes

Step-by-step explanation:

M2 = M1(0.5)^t/t1/2

M2 (mass after time t) = 26 g

M1 ( initial mass) = 670 g

t1/2 (half life) = 11 min

t (time required for Element X to decay to M2)

M2/M1 = (0.5)^t/t1/2

26/670 = (0.5)^t/11

0.039 = (0.5)^t/11

ln 0.039 = t/11 ln 0.5

t = 11 ln 0.039/ln 0.5 = -35.686/-0.693 = 51.5 minutes