A doctor prescribes 200 mg of medication on the first day of treatment. The dosages is halved on each successive day for one week. To the nearest milligram, what is the total amount of medication administered?
396mg
To find the total amount of medication administered, we need to calculate the sum of the dosages for each day.
Here's the breakdown of the dosages over one week:
Day 1: 200 mg
Day 2: 200 mg / 2 = 100 mg
Day 3: 100 mg / 2 = 50 mg
Day 4: 50 mg / 2 = 25 mg
Day 5: 25 mg / 2 = 12.5 mg
Day 6: 12.5 mg / 2 = 6.25 mg
Day 7: 6.25 mg / 2 = 3.125 mg
To find the total amount, we add up the dosages for each day:
200 + 100 + 50 + 25 + 12.5 + 6.25 + 3.125 ≈ 396.875 mg
Therefore, to the nearest milligram, the total amount of medication administered over one week is approximately 397 mg.
To find the total amount of medication administered over one week, we need to calculate the sum of the medication doses for every day.
Let's break down the problem and calculate each day's dosage:
Day 1: 200 mg
Day 2: The dosage is halved, so it becomes 200 mg / 2 = 100 mg
Day 3: Again, the dosage is halved, so it becomes 100 mg / 2 = 50 mg
Day 4: Dividing the previous day's dosage by 2 gives us 50 mg / 2 = 25 mg
Day 5: Continuing the pattern, the dosage would be 25 mg / 2 = 12.5 mg
Now, at this point, we need to clarify if the dosage is rounded to the nearest milligram or if decimal values are allowed. If decimal values are allowed, we would have:
Day 6: Halving 12.5 mg would give us 12.5 mg / 2 = 6.25 mg
Day 7: Again, halving 6.25 mg would give us 6.25 mg / 2 = 3.125 mg
However, since we are asked to round to the nearest milligram, we will round the decimal values:
Day 6: Rounding 6.25 mg to the nearest milligram gives us 6 mg
Day 7: Rounding 3.125 mg to the nearest milligram gives us 3 mg
Now we can sum up all the daily dosages:
200 mg + 100 mg + 50 mg + 25 mg + 12.5 mg + 6 mg + 3 mg = 396.5 mg
Rounding to the nearest milligram, the total amount of medication administered over one week is 397 mg.
Sum(all terms) = a/(1-r)
= 200/(1/2)
= 400