(*exponencialny trend*)

T[t_,alfa_,beta_]:=alfa beta^t;

Plot[T[x,0.2,4],{x,0,1}]

(*LogisticTrend[t_,alfa_,beta_,gama_]:=(gama/(1+alfa beta^t));*)

(*Plot[LogisticTrend[x,0.2,4,1],{x,0,1}]*)

derlogist[t_,alfa_,beta_,gama_]:=D[LogisticTrend[t,30,0.95,1],t]

Plot[derlogist[x,30,0.95,1],{x,1,10}]

derlogist[x,1,4,1]

Solve[-(((4^x) Log[4])/(((1+(4^x)))^2))==0]

LogisticTrend[t]:=(1/(1+30 0.95^t));
Plot[LogisticTrend[x],{x,0,200}]

Plot[(1/(1+30 0.95^t)),{t,0,200}]

D[(1/(1+30 0.95^t)),t]

Plot[((1.5387988316265173` ((0.95`)^t))/(((1+30 ((0.95`)^t)))^2)),{t,0,200}]

Solve[D[(1/(1+30 0.95^t)),{t,2}]==0]

Limit[(1/(1+30 2^t)),t->Infinity]

Limit[(1/(1+30 0.95^t)),t->Infinity]

Plot[E^(2-2 0.95^t),{t,0,200}]

gompertz[t]=E^(2-2 0.95^t)

D[(E^(2-2 (0.95^t))),t]

Plot[0.10258658877510116 (0.95^t) (E^(2-2 ((0.95`)^t))),{t,0,200}]

D[(E^(2-2 (0.95^t))),{t,2}]

Plot[-0.0052620040982558555` ((0.95`)^t) (E^(2-2 ((0.95`)^t)))+0.010524008196511711` ((0.95`)^(2 t)) (E^(2-2 ((0.95`)^t))),{t,0,200}]

Solve[D[(E^(2-2 (0.95^t))),{t,2}]==0]

TT[t_]:=E^(g+a b^t)

D[TT[x],x]

D[TT[x],{x,2}]