Question

If a person has a \(50 \%\) increase in insulin sensitivity, what happens to insulin release for the person to remain in the normal curve?

Short answer

For the person with a 50% increase in insulin sensitivity, their insulin release should be \(\frac{2}{3}\) of their original insulin release. This means that the person's body will need to release 33.33% less insulin than before to maintain their blood sugar levels in the normal range.

Step-by-step solution

Understand the relationship between insulin sensitivity and insulin release

Insulin sensitivity represents how well a person's body responds to insulin, which helps regulate blood sugar levels. It is the relationship between insulin levels (insulin release) and how well the body processes glucose. When insulin sensitivity increases, the body can effectively use insulin with a lower insulin release. Conversely, if insulin sensitivity decreases, more insulin needs to be released to keep blood sugar levels in check.

Analyze the given increase in insulin sensitivity

The problem states that there is a 50% increase in insulin sensitivity. This means that the person's body is now 1.5 times as sensitive to insulin as it was before. The new insulin sensitivity can be written as 1.5 * S, where S is the initial insulin sensitivity.

Determine the change in insulin release needed to maintain normal curve

To keep the person in the normal curve, we need to maintain a balance between insulin sensitivity and insulin release. Since insulin sensitivity has increased, the insulin release should decrease to maintain the balance. Let R_new represent the new insulin release, and R_original represent the original insulin release. We can set up an equation to represent the balance: R_original * S = R_new * (1.5 * S)

Solve for the new insulin release

We can divide both sides of the equation by S to remove it from the equation: R_original = R_new * 1.5 Now divide both sides by 1.5 to solve for R_new: R_new = R_original / 1.5 This equation shows that the new insulin release is 2/3 of the original insulin release to maintain the person in the normal curve.

Interpret the results

Since the person has a 50% increase in insulin sensitivity, they can effectively use insulin with a lower insulin release. To maintain their position in the normal curve, their insulin release should be 1/1.5 or 2/3 of their original insulin release. This means that the person's body will need to release 33.33% less insulin than before to maintain their blood sugar levels in the normal range.