A tank of water drains at a constant rate. The table shows the number of gallons of water left in the tank after two different amounts of time. if the time is 10 minutes and theres 450 gallons in the tank and at 30 minutes there's 330 Write a function notation to model y, the total volume of water remaining in the tank after x minutes of draining.
The function notation to model y, the total volume of water remaining in the tank after x minutes of draining, can be written as:
y(x) = mx + b
where:
m is the rate at which the water is draining (gallons per minute), and
b is the initial volume of water in the tank (gallons) before any draining.
To find m and b in this problem, we can use the given information from the table:
When x = 10 minutes, y(10) = 450 gallons.
When x = 30 minutes, y(30) = 330 gallons.
Using these data points, we can set up two equations to solve for m and b:
450 = 10m + b
330 = 30m + b
Solving these two equations will give us the values for m and b, which can then be used in the function notation y(x) = mx + b.