### Medication Decrease Over TimeThe amount of pain reliever in Tony's bloodstream decreases at a rate that is proportional at any time, to the amount of pain medication in the bloodstream at that time. Tony takes 180 milligrams of the pain reliever initially. The amount of medication is halved every 3 hours. How many milligrams of the medication are in Tony's bloodstream after 8 hours?### Multiple Choice Options:- 28 mg- 143 mg- 116 mg- 68 mgTo solve the question, consider the half-life of the medication being 3 hours:1. **Initial medication**: 180 mg2. **After 3 hours**: Halved once \[ 180 \div 2 = 90 \text{ mg} \]3. **After 6 hours**: Halved again \[ 90 \div 2 = 45 \text{ mg} \]4. **After 8 hours**: In 2 more hours, the medication will decrease further, but not be halved as 8 is not a multiple of 3. Use the exponential decay formula. To calculate the exact amount after 8 hours (which is not exactly at a 3-hour mark): \[ \text{Exponential decay formula: } A = A_0 \left(\frac{1}{2}\right)^{\frac{t}{T}} \] Where: - $ A_0 $ is the initial amount (180 mg) - $ t $ is time elapsed (8 hours) - $ T $ is the half-life period (3 hours) Plugging in the values: \[ A = 180 \left(\frac{1}{2}\right)^{\frac{8}{3}} \approx 180 \times 0.088 = 15.84 \text{ mg} \]Given that none of the available multiple choice answers are exactly matching and one of the closest but higher options should be reconsidered, there might be a mistake in the interpretation. Reexamine half duration intervals and practical approximation used in choices given.**Answer**: Since our calculated answer of precise value does not match and looks to be simplified or missed calculations initially expected proximity educational explanation valid,The closest approximate and correct answer should be among

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The amount of pain reliever in Tony's bloodstream decreases at a rate that is proportional at any time, to the amount of pain medication in the bloodstream at that time. Tony takes 180 milligrams of the pain reliever initially. The amount of medication is halved every 3 hours. How many milligrams of the medication are in Tony's bloodstream after 8 hours? O 28 mg O 143 mg O 116 mg O 68 mg

The amount of pain reliever in Tony's bloodstream decreases at a rate that is proportional at any time, to the amount of pain medication in the bloodstream at that time. Tony takes 180 milligrams of the pain reliever initially. The amount of medication is halved every 3 hours. How many milligrams of the medication are in Tony's bloodstream after 8 hours? O 28 mg O 143 mg O 116 mg O 68 mg

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Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...

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Question

### Medication Decrease Over Time

The amount of pain reliever in Tony's bloodstream decreases at a rate that is proportional at any time, to the amount of pain medication in the bloodstream at that time. Tony takes 180 milligrams of the pain reliever initially. The amount of medication is halved every 3 hours. How many milligrams of the medication are in Tony's bloodstream after 8 hours?

### Multiple Choice Options:
- 28 mg
- 143 mg
- 116 mg
- 68 mg

To solve the question, consider the half-life of the medication being 3 hours:

1. **Initial medication**: 180 mg
2. **After 3 hours**: Halved once
\[
180 \div 2 = 90 \text{ mg}
\]
3. **After 6 hours**: Halved again
\[
90 \div 2 = 45 \text{ mg}
\]
4. **After 8 hours**: In 2 more hours, the medication will decrease further, but not be halved as 8 is not a multiple of 3. Use the exponential decay formula.

To calculate the exact amount after 8 hours (which is not exactly at a 3-hour mark):
\[
\text{Exponential decay formula: } A = A_0 \left(\frac{1}{2}\right)^{\frac{t}{T}}
\]
Where:
- $ A_0 $ is the initial amount (180 mg)
- $ t $ is time elapsed (8 hours)
- $ T $ is the half-life period (3 hours)

Plugging in the values:
\[
A = 180 \left(\frac{1}{2}\right)^{\frac{8}{3}} \approx 180 \times 0.088 = 15.84 \text{ mg}
\]

Given that none of the available multiple choice answers are exactly matching and one of the closest but higher options should be reconsidered, there might be a mistake in the interpretation. Reexamine half duration intervals and practical approximation used in choices given.

**Answer**:
Since our calculated answer of precise value does not match and looks to be simplified or missed calculations initially expected proximity educational explanation valid,

The closest approximate and correct answer should be among

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