Final answer:
When x increases by 15%, y decreases to approximately 86.96% of its original value because y is inversely proportional to x.
Step-by-step explanation:
If y is inversely proportional to x, it means that y = k/x, where k is a constant. If the value of x is increased by 15%, the new value of x becomes x multiplied by 1.15. Since y is inversely proportional to x, the value of y will decrease. To find the exact new value of y, you can use the following relationship:
- Original equation: y = k/x
- After a 15% increase in x: y' = k/(1.15x)
By comparing the original and new equations, you can see that the new value of y, denoted y', is approximately 86.96% of the old value (since 1/1.15 is approximately 0.8696). So, when x increases by 15%, y decreases to roughly 86.96% of its original value.