Question

At time t​=0, water begins to drip out of a pipe into an empty bucket. After 98 ​minutes, there are 14 inches of water in the bucket. Write a linear function rule to model how many inches of water w are in the bucket after any number of minutes t.

Answer 1

To model the amount of water in inches w as a function of the time in minutes t, we derive a linear equation using the slope of 1/7 inches per minute from the given points, and obtain the formula w = (1/7)t.

Step-by-step explanation:

The student is asked to write a linear function rule to model the relationship between the number of minutes t and the inches of water w in the bucket. The linear equation can be determined using the point (98, 14) and the initial condition (0, 0).

Step-by-Step Solution:

Identify the slope (rate): Since the bucket starts empty, our starting point is (0, 0). After 98 minutes, there are 14 inches of water, represented by the point (98, 14). The slope m is the change in water level over the change in time, which is (14 - 0)/(98 - 0) = 14/98, which simplifies to 1/7 inches per minute.

Write the equation using the slope-intercept form y = mx + b, where m is the slope and b is the y-intercept. Since the y-intercept represents the starting amount of water, which is zero, the formula simplifies to w = (1/7)t.

This equation represents a direct proportionality between the time in minutes t and the water level in inches w.