Solve[x*Exp[(1-x)/0.75]==1,x]

Plot[Floor[32*(0.466996*Exp[x*(1-0.466996)/0.70])]/32,{x,0,1},PlotRange->{0,1}]

36^8/(3600*1000000.0)

0.00128357*Exp[(1-0.00128357)/0.15]

Floor[2.3]

lambda1[p_]=Last[First[First[Solve[x*Exp[(1-x)/p]==1,x]]]]

Plot[Floor[128*lambda1[p]],{p,0.01,0.99}]

Plot[Last[First[FindRoot[Floor[k*lambda1[p]]==1,{p,0.01,0.99}]]],{k,1,128}]

lambda1[0.5]

Last[Last[FindRoot[x*Exp[(1-x)/0.5]==1,{x,0,0.99999}]]]

Last[First[First[Solve[x*Exp[(1-x)/0.75]==1,x]]]]

Plot[2^x*Log[2]/0.01,{x,0,1}]

Solve[x*Exp[(1-x)*(1+t)]==1,x]

a=Last[Last[Last[%]]]

Simplify[a*Exp[(1-a)*(1+t)*y]]

Plot[ProductLog[x],{x,-2,5}]

Plot[x*Exp[x],{x,0,2}]

Solve[Log[x]/b+1==x,x]

Solve[Log[x]/(1+0.9)+1==x,x]

N[%]

Plot[{0.5*Log[x]+1,x},{x,0,4}]

Plot[1/(1+x),{x,0,1}]

dru[t_]=a

dru[1]

Solve[h*Exp[(1-h)*(1+t)]==1,h]

a

Plot[dru[t/100],{t,0,20}]

dru[0.9]

Plot[ProductLog[x],{x,-2,5}]

dru[t]

final[x_,t_]=dru[t]*Exp[(1-dru[t])*(1+t)*x]

Plot[{final[x,0.1],final[x,0.2],final[x,0.3],final[x,0.5],final[x,1]},{x,0,1},PlotRange->{{0,1},{0,1}}]

Series[final[0,t],{t,0,2}]

1/(1-dru[0.01])

Plot[1/(1-dru[t/100]),{t,0,100},PlotRange->{{0,100},{0,10}}]

Series[1/(1-dru[t]),{t,0,2}]

Series[dru[t],{t,0,1}]

Plot[dru[t],{t,0,0.3}]

D[dru][t]

dru[t]

Plot[{final[0,0.1],final[x,0.2],final[x,0.3],final[x,0.5],final[x,1]},{x,0,1},PlotRange->{{0,1},{0,1}}]

Plot[final[0,x],{x,0.1,1}]

N[1000000/48000]