ODE Decay Question :
In the rock being examined there is 100 mg of uranium and 14 mg of lead. Uranium decays with a half-life of 4.5 *10^9 years and after full decay of 238g of uranium 206 g of lead is left. Determine the rock age. Assume that when the rock formed it contained no lead, and neglect all intermediate decay-chain elements( since their half-life is much smaller than uranium )

Question

ODE Decay Question :
In the rock being examined there is 100 mg of uranium and 14 mg of lead. Uranium decays with a half-life of 4.5 *10^9 years and after full decay of 238g of uranium 206 g of lead is left. Determine the rock age. Assume that when the rock formed it contained no lead, and neglect all intermediate decay-chain elements( since their half-life is much smaller than uranium )

anonymous · Answer

the amount of lead formed is proportional to the amount of Uranium left.  the amount of uranium left is equal to the original amount minus the amount decayed. ie
 $$Pb(t)=K*U(t)$$  for any t, and  $$U(t)= U(0)- U(0)*\left( \frac{ 1 }{ 2} \right)\ ^{-\frac{ t }{ HL }} $$ Can you take it from here ?