In dogs, the drug carprofen has a half-life of 8 hours. If a veterinarian gives a dog an 80-milligram dose, how long will it take for the amount of carprofen in the dog to reach 10 milligrams?
The formula for half-life is given by: N(t)=Ne^(-λt) or N(t)=N(1/2)^(t/τ) where: t=time N=initial amount N(t)=final amount τ=half-life thus the time taken for the drug to decay will be: 10=80(1/2)^(t/8) 1/8=(1/2)^(t/8) introducing natural logs; ln (1/8)=(t/8)ln (1/2) thus; [ln 1/8]/[ln 1/2]=t/8 3=t/8 t=3*8 t=24 hours the answer is 24 hours
