Question

Element X is a radioactive isotope such that every 61 years, its mass decreases by half. Given that the initial mass of a sample of Element X is 30 grams, how long would it be until the mass of the sample reached 22 grams, to the nearest tenth of a year?

Answer 1

27.3

Explanation:

y=a(1/2)^t/h

Plug in

22=30(1/2)^t/61

Divide both sides by 30

0.7333333333=(1/2)^t/61

Log both

Log(0.7333333333) / Log(1/2)

0.447458977 = t/61

0.447458977 x 61 = t

27.2949976 to the nearest tenth is 27.3 = t