衰變速度= dM/dt,由條件得知,
{dM/dt = -λM,λ是衰變系數(shù),且λ>0
{M|(t=0) = M₀ ...(#)
解微分方程dM/dt = -λM
dM/M = -λ•dt
ln|M| = -λt + C
M = e^(-λt + C)
即M = Ce^(-λt),再代入(#)的條件,
當(dāng)t = 0時(shí)M = M₀
M₀ = C(e^0) = C
所以衰變方程為M = M₀e^(-λt)