tau=10^9;(* in unit of yr *)
Ncap[t_]:= Exp[-t/tau];
Plot[Ncap[t],{t, 0, 10tau},PlotRange->All]

DSolve[ NN'[t] == -(1/tau)NN[t] ,NN[t],t]

DSolve[y'[x] == x y[x] ,y[x],x]

tau=10^9;
sol=NDSolve[ {NN'[t] == -(1/tau)NN[t] ,NN[0]==10^20},NN,{t,0,20tau}];
NNsol[t_]:=Evaluate[NN[t]/.sol][[1]];
Plot[NNsol[t],{t,0,10tau}]

omega=1;T = 2Pi/omega;
NDSolve[{theta''[t]==omega^2 theta[t],theta[0]==5Degree,theta'[0]==0},theta,{t,0,10T}]