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Graph of line and scatter plot. X-axis as Time (minutes). Y-axis as Water (gallons). The line begins at (0, 120) slants down till (70, 30). 10 closed circles plotted at (4, 117), (9, 103), (15, 102), (20, 98), (24, 85), (30, 82) through (60, 49).
The scatter plot shows the amount of water in a tank as measured every few minutes.
The initial amount of water in the tank was
gallons. The line of best fit shows that about
gallon(s) of water were lost per minute. The tank will be empty in about
minutes.
The initial amount of water in the tank was 120 gallons. The line of best fit shows that about 1.4 gallon(s) of water were lost per minute. The tank will be empty in about 75 minutes.
The initial amount of water in the tank was 120 gallons. The line of best fit shows that about 1.9 gallons of water were lost per minute. The tank will be empty in about 63 minutes.
To answer these questions, we need to carefully analyze the given information and observations provided in the graph.
1. The initial amount of water in the tank:
According to the graph, the line begins at (0, 120). This means that at the start (0 minutes), there were 120 gallons of water in the tank. Therefore, the initial amount of water in the tank was 120 gallons.
2. The amount of water lost per minute:
By examining the slope of the line, we can determine the amount of water lost per minute. Looking at the endpoints of the line, it slants down from (0, 120) to (70, 30). To find the amount of water lost, we can subtract the initial amount from the final amount and divide it by the time it took to lose that amount.
Final amount of water = 30 gallons
Initial amount of water = 120 gallons
Time elapsed = 70 minutes
Water lost per minute = (Final amount - Initial amount) / Time elapsed
Water lost per minute = (30 - 120) / 70
Water lost per minute = -90 / 70
Water lost per minute ≈ -1.29 gallons
Therefore, the line of best fit shows that approximately 1.29 gallons of water were lost per minute.
3. Time until the tank is empty:
To assess how long the tank will be empty, we can analyze the scatter plot with the closed circles. The scatter plot represents measurements taken over time, indicating the water levels at specific intervals.
By observing the scatter plot, it's evident that the points start at (4, 117) and progressively decrease until they reach (60, 49). From these two points, we can conclude that the water level decreases by about 68 gallons over 56 minutes.
Water level decrease = Initial amount - Final amount
Water level decrease ≈ 117 - 49 ≈ 68 gallons
Time elapsed = 60 - 4 = 56 minutes
Based on this information, we can estimate the time until the tank is empty by dividing the remaining water level by the rate of water loss per minute.
Time until the tank is empty = Remaining water / Water loss per minute
Time until the tank is empty = 49 gallons / 1.29 gallons per minute
Time until the tank is empty ≈ 38.01 minutes
Therefore, the tank will be empty in approximately 38 minutes.