The half life of a medication is the time it takes for the medication to reduce to half of its original amount in a patient's bloodstream. a certain antibiotic has a half-life of about 8 hours. a patient is administrated 500 miligrams of the medication. write a function that models the amount of the medication in the patients bloodstream over time

Step-by-step explanation:

Half life of an antibiotic is 8 hours so the sequence formed at every 8 hours showing the amount of drug in the blood stream will be

Time                                  0        8         16        32  

Concentration in blood 500    250     125     62.5

(in mg)

We can see from the table that the sequence formed is geometric in nature.

So the explicit formula for this sequence will be

Where = Amount of drug in the blood after time t hours

= Loading dose

r = Common ratio of the sequence

t = time or duration

From this sequence r =

Therefore, the explicit formula will be

We can rewrite the formula in the form a function

answer: 59

step-by-step explanation: