w[i_,t_]:=a/(1+(a/x[i] -1) E^(-c t));
x[i_]=10+i 10;
c=0.5;
a=100;
abb=Plot[Evaluate[Table[w[i,t],{i,0,12}]],{t,0,10},
AxesLabel->{"t","x"},ImageSize->{400,300}];