Question

A doctor prescribes 500 milligrams of a therapeutic drug that decays by about 19% each hour.

a) To the nearest minute, what is the half-life of the drug?
b)
Write an exponential model representing the amount of the drug remaining in the patient's
system after t hours. (2 points)
c)
Use your formula to find the amount of drug that would remain in the patient's system after 24
hours. Round your answer to the nearest hundredth of a gram. (2 points)

Answer 1

a) half life is 3h 17 minutes

b) function of residue drug after t hours with initial quantity = 500 mg

f(t) = 500 (0.81^t)

c) drug left in patient's system after 24 hours

= 0.00 grams (to the hundredth of a gram.

Explanation:

Given:

Drug initial active weight, A = 500 mg

Residue active weight, f(t) = A 0.81^t

t = time in hours.

a) half life

Half life is T, such that f(T) = 0.5A =>

0.5A = A(0.81^t)

0.81^t = 0.5

t*log(0.81) = log(0.5)

t = log(0.5) / log(0.81) = -0.6931 / -0.2107 = 3.2894 hours

= 3 h 17.36 minutes

b) Equation of function of residue drug as a function of time t in hours

A=500 mg

f(t) = A(0.81^t) substitute A = 500 mg

= 500(0.81^t) mg

c) weight of residue drug after 24 hours to the hundredth of a gram.

t=24 hours

A=500

f(t) = 500(0.81^t) substitute t=24 hours

= 500(0.81^24)

= 3.181 mg

= 0.003181 g