Question

Dr. Santiago is contemplating the impact of an antibiotic on a particular patient. The patient

will take 840 milligrams, and every hour his body will break down 45% of it. How much will
be left after 5 hours?
If necessary, round your answer to the nearest tenth.

Answer 1

Explanation:

If his body is breaking down 45% of the medicine, it is losing 100% - 45% = 55%. This means that while he is LOSING 45% of the medicine, he is KEEPING 55% of it. This is an exponential function of the type

`y=a(b)^x` where y is the amount of medicine after the increase or decrease (b) of the original amount, a. The number of hours is represented by x.

Our original amount is 840 mg, so a = 840. And if we are losing .45, we are retaining .55, so b = .55. The model for this situation is

`y=840(.55)^x`

If we want to find out how much medicine is left after 5 hours, we sub in a 5 for x and solve for y:

`y=840(.55)^5` and

y = 840(.0503284375) so

y = 42.2758875 or, rounded to the nearest tenth,

y = 42.3 mg