Question

Below are descriptions of four situations in which the volume of water in a tank is a function of time. Which of these descriptions matches the graph shown?

Option 1: An empty 20-gallon water tank is filled at a constant rate for 3 minutes until it is half full. Then, it is emptied at a constant rate for 3 minutes.

Option 2: A full 10-gallon water tank is drained for 30 seconds until it is half full. Afterwards, it gets refilled.

Option 3: A 2,000-gallon water tank starts out empty. It is being filled for 5 hours, slowly at first, and faster later.

Option 4: An empty 100-gallon water tank is filled in 50 minutes. Then, a dog jumps in and splashes around for 10 minutes, letting 7 gallons of water out. The tank is refilled.

Answer 1

Considering the problem, the description of each option suggests different graphical representations of how the volume changes over time. However, without the specific graph, a definitive answer cannot be provided. Understanding of volume flow rates and changing rates over time is key to solving this type of problem.

Step-by-step explanation:

The question relates to situations where the volume of water in a tank changes over time and which description matches a given graph. To answer the initial question:

Option 1 describes a 20-gallon tank that is being filled for 3 minutes until half full and then emptied for 3 minutes at a constant rate. This situation would likely produce a linear graph that increases and then decreases at the same rate.

Option 2 involves a 10-gallon tank drained for 30 seconds until half full and then refilled, which suggests an initial sharp decrease followed by an increase in the water level.

Option 3 refers to a large 2,000-gallon tank filled over 5 hours, starting slowly and then speeding up. This would create a graph where the slope (rate of volume change) increases over time.

Option 4 presents a 100-gallon tank filled over 50 minutes with an interruption caused by a dog. The graph would show a steady increase, a shorter period of decline, and then an increase again.

Without the specific graph mentioned in the question, we cannot determine which option matches the graph. More information would be needed for an accurate answer. The volume flow rate and the concept of filling and draining rates are essential elements of this problem.