A -gram sample of a radioactive isotope decays so that its mass (in grams) at time…
MATHEMATICS · Multi-part · AP · Calculus AB · Differential Equations · Differential Equations
Problem
A 2-gram sample of a radioactive isotope decays so that its mass m(t) (in grams) at time t (in years) satisfies dtdm=km. After 4 years, the sample’s mass is measured to be 1.2 grams.
(a) Calculate the decay constant k for the isotope. Include appropriate units in your answer.
(b) Regulations require storage of the isotope in a special container whenever the mass is between 0.25 g and 1.0 g. Determine the closed time interval, measured from t=0, during which the sample mass lies within this range.
(c) Explain why the interval found in part (b) is finite even though radioactive decay is an ongoing process.