Final answer:
The linear function rule that models the amount of water w in inches in the bucket after t minutes is w = 0.2t, with a slope of 0.2 representing the rate of water dripping into the bucket.
Step-by-step explanation:
To write a linear function that models the situation where water drips into a bucket, we need two pieces of information: the rate at which the water drips (called the slope of the linear function), and the initial amount of water in the bucket (called the y-intercept).
According to the information provided, at time t=0, the bucket is empty, which means the y-intercept is 0. After 40 minutes, there are 8 inches of water in the bucket. Therefore, the slope, which represents the inches of water per minute, can be calculated as the change in water level over the change in time, which is 8 inches over 40 minutes or 0.2 inches per minute.
The linear function rule to describe this situation is w = 0.2t. This means that after any number of minutes t, the number of inches w of water in the bucket can be found by multiplying the time t in minutes by 0.2.