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malfutka [58]
3 years ago
8

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

Mathematics
1 answer:
Savatey [412]3 years ago
3 0

Answer:

Step-by-step 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

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