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