Calcium-47, which decays by beta emission, has a half-life of 4.5days:How many milligrams of an initial 24mg of calcium-47 remain after 36days?

How many days are required for 9.60mg of calcium-47 to decay to 1.2mg?

For radioactive decay:

N = N (0) x exp (-λt), where λ is the decay constant equivalent to ln (2) / half life, N is the amount after a given amount of time, t is the time passed and N (0) is the initial amount.

1)

N = 24 x exp (-ln (2) / 4.5 x 36)

N = 0.09375 mg

2)

1.2 = 9.6 x exp (-ln (2) / 4.5 x t)

ln (1.2/9.6) = - t x ln (2) / 4.5

t = 13.5 days