A sample of the medical tracer iodine-131 decays according to

PHYSICS · Subjective · Fermi University Physics · Mathematical Methods for Physics · Ordinary differential equations · Ordinary differential equations

Mathematical Methods for Physics, Ch First-order differential equations and physical modelling

Problem

A 5.00 g5.00\,\mathrm{g} sample of the medical tracer iodine-131 decays according to N˙=−λN\dot{N} = -\lambda N, where N(t)N(t) is the mass of iodine-131 remaining and λ\lambda is its decay constant. The half-life of iodine-131 is 8.02 days8.02\,\mathrm{days}. Solve the equation with N(0)=5.00 gN(0) = 5.00\,\mathrm{g} and find the time at which only 0.500 g0.500\,\mathrm{g} remains.

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