Final answer:
The number of cats and the time it takes to use a 5 lb bag of cat food are inversely proportional; as the number of cats increases, the time decreases such that their product remains constant.
Step-by-step explanation:
Two quantities are inversely proportional if as one quantity increases, the other decreases in such a way that the product of the two remains constant. This can be described using the equation y = k/x, where k remains constant while x and y vary. When we consider the scenario of a fixed amount of cat food and multiple cats, the number of days it takes to use up the 5 lb bag of food becomes inversely proportional to the number of cats. If each cat eats the same amount of food per day, having more cats will result in the food being used up more quickly, and vice versa.
Let's say it takes 10 days for one cat to eat a 5 lb bag of cat food. If two cats are eating, it would take 5 days for them to finish the same amount of food. Therefore, if t represents the time it takes and c represents the number of cats, we have t = k/c where k is a constant representing the product of the initial time duration and the starting number of cats (10 days * 1 cat).