Double_t expFunc(Double_t *x, Double_t *par) {
  return par[0]*TMath::Exp(-par[1]*x[0]);
}

Int_t main(){
  TFile *fin = new TFile("exp.root", "read");
  TH1F *h = (TH1F*)fin->Get("h");
  h->Draw();

  TF1 *func = new TF1("func", expFunc, 1., 5., 2);
  func->SetParameters(2000.,0.4);
  h->Fit("func","R");
  func->Draw("same");
}