Answer:
[tex]w=0.5t[/tex]
Step-by-step explanation:
Given:
'w' represents inches of water left after 't' minutes of time.
The dripping out of water is a linear function.
At time 't' equal to 0, the bucket was empty.
After 14 minutes, there are 7 inches of water in the bucket.
A linear function model is of the form: [tex]w=mt+b[/tex]
[tex]Where, m\to\textrm{dripping rate of water}\\b\to\textrm{water level at t=0}[/tex]
Now, at [tex]t=0,w=0(\textrm{As bucket was empty})[/tex]
At [tex]t=14,w=7[/tex]
Therefore, plugging these values in the above linear model and solving the system of linear equations. This gives,
[tex]0=m(0)+b\\0=0+b\\b=0\\\\7=14m+0\\m=\frac{7}{14}=0.5\ in/min[/tex]
Therefore, the values of 'm' and 'b' are 0.5 and 0 respectively.
Thus, the linear model is given as:
[tex]w=0.5t[/tex]
