Answer:
The linear function of the bucket is , where
represents the amount of water, measured in inches, and
is the time, measured in minutes.
Step-by-step explanation:
According to the Euclidean and Analytical Geometries, we can construct a line by knowing two distinct points on a plane. Besides, we know two different conditions for the bucket:
Initial condition of the bucket
Final condition of the bucket
The equation of the line is defined by the following model:
(1)
Where:
- Independent variable, dimensionless.
- Dependent variable, dimensionless.
- y-Intercept, dimensionless.
- Slope, dimensionless.
Based on the known conditions of the bucket, we obtain the following system of linear equations:
(2)
(3)
The solution of the system of equations is:
and
Then, the linear function of the bucket is , where
represents the amount of water, measured in inches, and
is the time, measured in minutes.