Jada fill the bathtub before taking a bath and then allows the water to drain when she’s done the graph below models the number of gallons of water. Why in the bathtub overtime TM minutes is the number of gallons of water in the bathtub a function of time.
The graph below models the number of gallons of water in the bathtub over time:
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In this graph, the vertical axis represents the number of gallons of water in the bathtub, and the horizontal axis represents time in minutes (labeled as TM in the question).
The graph shows that the number of gallons of water in the bathtub decreases over time as the water drains out. Hence, the number of gallons of water in the bathtub is a function of time.
The number of gallons of water in the bathtub over time, in TM minutes, is a function of time because there is a clear relationship between the two variables. As time progresses, the number of gallons of water in the bathtub changes. This change can be observed and measured, and it is possible to determine the number of gallons of water in the bathtub at any given point in time. Therefore, the situation can be represented by a function, where the input variable is time (TM minutes) and the output variable is the number of gallons of water in the bathtub.
To understand why the number of gallons of water in the bathtub is a function of time, we need to explore the concept of a function and how it applies in this scenario.
A function is a relationship where each input (independent variable) is associated with exactly one output (dependent variable). In this case, the independent variable is time, represented as "TM minutes," and the dependent variable is the number of gallons of water in the bathtub.
In the given scenario, Jada fills the bathtub before taking a bath and allows the water to drain when she's done. The graph provided models the number of gallons of water in the bathtub over time. Let's assume the graph shows the number of gallons on the vertical axis and time on the horizontal axis.
As time (TM minutes) progresses, the number of gallons of water in the bathtub changes. At the beginning, the bathtub is empty, so there are zero gallons of water. As Jada starts filling the tub, the number of gallons increases, and when she turns off the water, it reaches its maximum capacity. Then, as time passes, the water drains out, and the number of gallons decreases until the bathtub is empty again.
Since the number of gallons in the bathtub changes based on the time elapsed, it is a clear example of a function. Each value of time (TM minutes) corresponds to a specific number of gallons in the bathtub. Consequently, we can define a function that relates time to the number of gallons of water:
Let's say "f(TM)" represents the number of gallons of water in the bathtub at a given time TM minutes. Then, f(TM) is a valid function because for each value of TM, there is precisely one corresponding value of f(TM).
Hence, in this scenario, the number of gallons of water in the bathtub is indeed a function of time.