An isotope has a half life of 1 day. If the initial mass of the isotope is 50mg, calculate the rate of change after the third day.

Answer 1

A = Pe^rt where t= time in days, r = decay rate measured in rate of change of grams per day

1/2 = e^r(1) = e^r

take natural logs of both sides

ln(1/2) =r

rate of decay = ln.5 = -0.693

on the 3rd day

A = 50e^-0.693(3) = 50e^-2.079

A= 6.25 mg left after 3 days

day zero 50 mg

day one 50/2 - 25 mg

day two 25/2 = 12.5 mg

day three 25/2 = 6.25 mg left

rate of change is -0.693 mg per day

or

A = Pe^-.693t

A = P(1/2)^t

A = 50(1/2)^3 = 50(1/8) - 6.25 mg left after 3 days