A person takes 200 milligrams of an antibiotic. Each hour, the remaining dosage in the person's blood stream decreases by 1/3.
Demitri and Kendal are trying to figure out how many milligrams are left in the person's bloodstream after 5 hours.
Demitri says that approximately 0.82 milligrams of the medication remains, because 200(1/3)^5 ≈0.82.
Kendal says that this can't be correct.
Who is correct and why? Select all correct answers
A) Demitri is correct. The equation 200(13)5≈0.82. is correct.
B) Demitri is correct. One-third of 200 is about 66.67. One-third of 66.67 is about 22.22. Do this a 3rd time and you get about 7.4. A 4th time gives you about 2.47. And a 5th time gives you about 0.82.
C) Kendal is correct. The fraction 13 is the rate of decay, not the growth factor.
D) Kendal is correct. If 200 decreases by 13, you get approx. 133.33. Do that again and you get about 88.89. Do that a 3rd time, you get about 59.29. A fourth time gives you about 39.51. And a 5th time gives you about 26.34.
I agree with Kendall because I when you decrease a number you are supposed to make it into a percentage, and then take away "1" which is what I did, and her answer ended up being correct. But I am not entirely sure it is.
amount remaining=original (2/3)^5=200*(2/3)^5=26.23 mg remains
and, you are correct.
To answer this question, let's go through the calculations step by step.
The remaining dosage in the person's bloodstream decreases by 1/3 each hour, which means each hour, the person retains 2/3 (1 - 1/3) of the previous amount.
We start with 200 milligrams, and after the first hour, the person retains (2/3) * 200 = 400/3 ≈ 133.33 milligrams.
After the second hour, the person retains (2/3) * 133.33 = 266.66/3 ≈ 88.89 milligrams.
After the third hour, the person retains (2/3) * 88.89 = 177.78/3 ≈ 59.26 milligrams.
After the fourth hour, the person retains (2/3) * 59.26 = 118.52/3 ≈ 39.51 milligrams.
After the fifth hour, the person retains (2/3) * 39.51 = 79.02/3 ≈ 26.34 milligrams.
So, the correct answer is:
D) Kendal is correct. After 5 hours, there are approximately 26.34 milligrams remaining in the person's bloodstream.