Answer :
To understand the given problem step-by-step, let's translate the data provided in the table into a more readable format and analyze it thoroughly.
### Step-by-Step Analysis:
1. Problem Overview:
A woman's blood glucose levels are measured over a period of time at different intervals (hours). We need to analyze the data to understand the trends and patterns in her blood glucose levels.
2. Given Data:
- Time Points (hours): [tex]\(0, 1, 2, 3, 4, 5\)[/tex]
- Blood Glucose Levels (mg/dl): [tex]\(100, 120, 110, 90, 80, 85\)[/tex]
This can be visualized as follows:
- At [tex]\(0\)[/tex] hours: Blood Glucose is [tex]\(100\)[/tex] mg/dl
- At [tex]\(1\)[/tex] hour: Blood Glucose is [tex]\(120\)[/tex] mg/dl
- At [tex]\(2\)[/tex] hours: Blood Glucose is [tex]\(110\)[/tex] mg/dl
- At [tex]\(3\)[/tex] hours: Blood Glucose is [tex]\(90\)[/tex] mg/dl
- At [tex]\(4\)[/tex] hours: Blood Glucose is [tex]\(80\)[/tex] mg/dl
- At [tex]\(5\)[/tex] hours: Blood Glucose is [tex]\(85\)[/tex] mg/dl
3. Data Interpretation:
- Initial Reading (0 hours): The initial blood glucose level is [tex]\(100\)[/tex] mg/dl.
- Peak Level (1 hour): The blood glucose level rises to [tex]\(120\)[/tex] mg/dl within the first hour, which is the peak.
- Declining Trend (2-4 hours): After the peak, the blood glucose level begins to drop:
- At [tex]\(2\)[/tex] hours: decreased to [tex]\(110\)[/tex] mg/dl
- At [tex]\(3\)[/tex] hours: further decreased to [tex]\(90\)[/tex] mg/dl
- At [tex]\(4\)[/tex] hours: reaches its lowest point at [tex]\(80\)[/tex] mg/dl
- Slight Increase (5 hours): At [tex]\(5\)[/tex] hours, the blood glucose level slightly increases to [tex]\(85\)[/tex] mg/dl.
4. Conclusion:
The data illustrates how the blood glucose level of the woman changes over time after initial testing. The glucose level peaks at [tex]\(1\)[/tex] hour post-testing, followed by a decline over the next [tex]\(3\)[/tex] hours, and then a small increase follows during the [tex]\(5^{th}\)[/tex] hour.
### Summary:
| Time (hours) | Blood Glucose (mg/dl) |
|------------------|---------------------------|
| 0 | 100 |
| 1 | 120 |
| 2 | 110 |
| 3 | 90 |
| 4 | 80 |
| 5 | 85 |
Each value in the table corresponds to the measurements provided. The trends should help in assessing the woman's blood glucose response over time, which might be essential for evaluating her metabolic status, potentially helping in diagnosing or managing diabetes mellitus.
### Step-by-Step Analysis:
1. Problem Overview:
A woman's blood glucose levels are measured over a period of time at different intervals (hours). We need to analyze the data to understand the trends and patterns in her blood glucose levels.
2. Given Data:
- Time Points (hours): [tex]\(0, 1, 2, 3, 4, 5\)[/tex]
- Blood Glucose Levels (mg/dl): [tex]\(100, 120, 110, 90, 80, 85\)[/tex]
This can be visualized as follows:
- At [tex]\(0\)[/tex] hours: Blood Glucose is [tex]\(100\)[/tex] mg/dl
- At [tex]\(1\)[/tex] hour: Blood Glucose is [tex]\(120\)[/tex] mg/dl
- At [tex]\(2\)[/tex] hours: Blood Glucose is [tex]\(110\)[/tex] mg/dl
- At [tex]\(3\)[/tex] hours: Blood Glucose is [tex]\(90\)[/tex] mg/dl
- At [tex]\(4\)[/tex] hours: Blood Glucose is [tex]\(80\)[/tex] mg/dl
- At [tex]\(5\)[/tex] hours: Blood Glucose is [tex]\(85\)[/tex] mg/dl
3. Data Interpretation:
- Initial Reading (0 hours): The initial blood glucose level is [tex]\(100\)[/tex] mg/dl.
- Peak Level (1 hour): The blood glucose level rises to [tex]\(120\)[/tex] mg/dl within the first hour, which is the peak.
- Declining Trend (2-4 hours): After the peak, the blood glucose level begins to drop:
- At [tex]\(2\)[/tex] hours: decreased to [tex]\(110\)[/tex] mg/dl
- At [tex]\(3\)[/tex] hours: further decreased to [tex]\(90\)[/tex] mg/dl
- At [tex]\(4\)[/tex] hours: reaches its lowest point at [tex]\(80\)[/tex] mg/dl
- Slight Increase (5 hours): At [tex]\(5\)[/tex] hours, the blood glucose level slightly increases to [tex]\(85\)[/tex] mg/dl.
4. Conclusion:
The data illustrates how the blood glucose level of the woman changes over time after initial testing. The glucose level peaks at [tex]\(1\)[/tex] hour post-testing, followed by a decline over the next [tex]\(3\)[/tex] hours, and then a small increase follows during the [tex]\(5^{th}\)[/tex] hour.
### Summary:
| Time (hours) | Blood Glucose (mg/dl) |
|------------------|---------------------------|
| 0 | 100 |
| 1 | 120 |
| 2 | 110 |
| 3 | 90 |
| 4 | 80 |
| 5 | 85 |
Each value in the table corresponds to the measurements provided. The trends should help in assessing the woman's blood glucose response over time, which might be essential for evaluating her metabolic status, potentially helping in diagnosing or managing diabetes mellitus.
