Question

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?

Answer 1

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