The halflife of cobalt 60 is 5 years a Obtain an exponential

The half-life of cobalt 60 is 5 years. a) Obtain an exponential model for cobalt 60 in the form Q(t) = Q_0 e^-kt. (Round coefficients to three significant digits.) b) Use your model to predict, to the nearest year, the time it takes for one third of the sample of cobalt 60 to decay.

Solution

a) k = ln(2)/T_half = ln(2)/5 = 0.13863

Q = Q₀e^-0.13863t

b) Q₀(1 - 1/3) = Q₀e^-0.13863t

ln(2/3) = -0.13863t

t = 2.9248 year