An inverse relationship exists when:
a. there is no association between two variables.
b. one variable increases and there is no change in the other variable.
c. one variable increases and the other variable increases.
d. one variable increases and the other variable decreases.
The correct answer and explanation is :
Correct Answer:
d. One variable increases and the other variable decreases.
Explanation:
An inverse relationship, also known as a negative correlation, occurs when two variables move in opposite directions. This means that as one variable increases, the other decreases, and vice versa. This relationship is commonly seen in economics, physics, and real-world scenarios.
For example, in economics, price and demand typically have an inverse relationship. When the price of a product increases, demand tends to decrease because consumers may look for substitutes or decide the product is too expensive. Conversely, when prices decrease, demand usually increases because consumers find the product more affordable.
Another example is speed and travel time. If a person increases their speed while traveling a fixed distance, the time taken to reach the destination decreases. Conversely, if speed decreases, the travel time increases.
Mathematically, an inverse relationship can be represented as:
[
y = \frac{k}{x}
]
where ( k ) is a constant. As ( x ) increases, ( y ) decreases, demonstrating an inverse relationship.
Inverse relationships are also seen in physics, such as Boyle’s Law, which states that for a fixed amount of gas at a constant temperature, pressure and volume have an inverse relationship. When the volume of a gas increases, its pressure decreases, and vice versa.
Understanding inverse relationships is crucial in various fields as they help in making predictions and informed decisions. Identifying these relationships allows researchers, businesses, and scientists to analyze trends, optimize strategies, and create efficient solutions.
