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The problem asks to estimate the rate of change of the concentration of glucose in a patient's blood at 120 minutes, using the tangent line drawn to the graph at that time. 

To estimate the rate of change:

1. The rate of change at a particular point on a graph is given by the slope of the tangent line at that point.
2. Slope = \( \frac{\text{change in y (glucose concentration)}}{\text{change in x (time)}} \).
3. From the graph, we can estimate two points along the tangent line at 120 minutes. These points can then be used to calculate the slope.

Looking at the image:

- One point on the tangent appears to be approximately \( (90 \, \text{min}, 180 \, \text{mg/dL}) \).
- Another point on the tangent appears to be roughly \( (150 \, \text{min}, 90 \, \text{mg/dL}) \).

Using these two points:
- \( \text{Slope} = \frac{90 - 180}{150 - 90} = \frac{-90}{60} = -1.5 \, \text{mg/dL per minute} \).

So, the rate of change of glucose concentration at 120 minutes is approximately **-1.5 mg/dL per minute**.

Would you like more details on how to approach similar problems, or do you have further questions?

Here are some related questions to explore:
1. How does the slope of a tangent relate to the concept of a derivative?
2. Why is the rate of change negative in this scenario?
3. How would the tangent line differ if it was drawn at a different time?
4. What does the graph suggest about glucose levels after drinking a glucose solution?
5. How could this analysis be useful in medical contexts?

**Tip**: Always choose two easily readable points on the tangent to calculate the slope for better accuracy.

The graph shows how the concentration of glucose in a patient's blood changes after they have drunk a glucose drink. A tangent is drawn to the graph at 120 minutes. Use the tangent to work out an estimate for the rate of change in concentration of glucose at 120 minutes.

Learn how to estimate the rate of change in glucose concentration at 120 minutes using the tangent line. This problem covers key concepts in calculating slopes and applying tangent line theorems, suitable for students in Grades 10-12.

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