calculate elimination rate constant
You can use this equation to very generally describe the one-compartment pharmacokinetics of a drug:

Cplasma = (Dose*F/Vd)e^(-kt)

Where F is the fraction that is bioavailable and Vd is the volume of distribution of the drug.  These values can be obtained from the Lexi-comp monograph.  If a drug is administered i.v., F = 1.  k in this equation is your elimination rate constant.



Your description of steady state is not correct.  Steady state is reached with multiple administrations of the drug after 3-5 half lives.  We usually assume steady state is reached in 5 half lives.  Here you are only dealing with one administration of the drug and a steady state is never reached.  The drug will be continuously cleared from plasma until Cplasma = 0.  The time that this takes is usually 5 half lives (50% of initial plasma concentration excreted after 1 half life, 75% after 2 half lives, 87.5% after 3 half lives, 93.75% after 4 half lives and 96.875% after 5 half lives).  



Without any plasma concentration data, a route of administration, volume of distribution and bioavailability, a proper elimination rate constant cannot be calculated.  Consider the case where an oral drug is only 75% bioavailable.  This means that 75% of the administered dose reaches the plasma and systemic circulation while 25% is cleared initially by stomach acid, digestion, poor absorption from the GI tract, etc.  The elimination rate constant for this drug will be different than for one that is 100% orally bioavailable.