Question

a swimming pool has about 603 cubic feet of water. the pool liner has a small hole and is leaking at a rate of 1.5 cubic feet each hour. ruby wrote the equation ( v(h)=-1.5h + 603 ) to represent the scenario. describe what each variable represents in the function, and how they relate to each other.

Explanation:

In the linear function \(v(h)= - 1.5h + 603\), the slope - intercept form of a linear equation is \(y = mx + b\), where \(m\) is the slope and \(b\) is the \(y\) - intercept.

• Variable \(h\):

The variable \(h\) represents the number of hours. Since the rate of water leakage is given as 1.5 cubic feet per hour, and the function is modeling the volume of water over time, the independent variable (the one that we can change freely) is the time in hours.

• Variable \(v(h)\):

The variable \(v(h)\) represents the volume of water in the pool. The function \(v(h)\) gives the amount of water remaining in the pool after \(h\) hours. The coefficient of \(h\) (\(-1.5\)) is the rate of change of the volume with respect to time. A negative value indicates that the volume is decreasing over time (because the pool is leaking). The constant term \(603\) is the initial volume of water in the pool (when \(h = 0\), \(v(0)=-1.5\times0 + 603=603\)).

Answer:

In the function \(v(h)=-1.5h + 603\), \(h\) represents the number of hours and \(v(h)\) represents the volume of water in the pool. The slope \(-1.5\) means the volume of water is decreasing at a rate of \(1.5\) cubic feet per hour, and the \(y\) - intercept \(603\) means the initial volume of water in the pool is \(603\) cubic feet.