Question

Paige is filling a 6.5 L bucket at a rate of 0.5 L per minute. What is the domain of the function that represents the volume of water in the bucket after x minutes if the bucket was empty when Paige arrived?

Answer 1

The domain of the function that represents the volume of water in a bucket being filled at a rate of 0.5 L per minute is [0, 13], which signifies the bucket can be filled for up to 13 minutes starting from empty to full.

Step-by-step explanation:

The domain of the function that represents the volume of water in the bucket after x minutes is the set of all possible values that x can take, given that Paige is filling a 6.5 L bucket at a rate of 0.5 L per minute, starting with an empty bucket. The function will start at x = 0, since the bucket is initially empty, and will end when the bucket is full at 6.5 L. As Paige fills the bucket at a rate of 0.5 L per minute, the bucket would be full in 13 minutes (6.5 L / 0.5 L per minute = 13 minutes). Therefore, the domain of the function is [0, 13]. This is the range of time in minutes during which Paige can be actively filling the bucket before it overflows.