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

So I think I found the decay equation U(t)= quantity of Uranium 
$$U(t)=U_{0}e^{\frac{\ln\frac{119}{238}}{4.5∗10^9}t}$$
 is this somewhat right? I then put 0.01 and t=4.5*10^9 to find the original amount of Uranium but I can't seem to get it right.

anonymous · Answer

so I got a slightly better equation $$U_{t}=U_{0}\exp(\frac{\ln(1/2)}{4.5*10^9}t)  $$