You took 140 mg of medicine yesterday. The half-life of this medicine is 14 hours. How much will be left in your system after 30 hours?

Question

You took 140 mg of medicine yesterday. The half-life of this medicine is 14 hours. How much will be left in your system after 30 hours?

Answer 1

fraction remaining = 0.5ⁿ where n = number of half lives that have elapsed (assuming a first order decay)

n = 30 hours/14 hours = 2.14 half lives

fraction remaining = 0.5^2.14

fraction remaining = 0.2269

mg remaining = 0.2269 x 140 mg = 31.8 mg (to 3 significant figures)

Answer 2

The formula for this exponential decay is: 140(0.5)^t/14 , where t denotes the elapse time in hours. Therefore, 30 hours later the amount left would be 140(0.5)^30/14 ≅ 31.7 mg (rounded to 1 decimal)