To analyze the point (t, w) = (6, 30) on the graph, we need to determine what this point indicates regarding water usage over time.
The point (6, 30) means that at 6 minutes (t = 6), 30 gallons of water have been used (w = 30).
From here, we can derive the average rate of water usage:
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If at t = 0 (the start time, which we can assume is 0 unless otherwise stated) the water usage was 0 gallons, then at t = 6 minutes, the usage is 30 gallons.
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The rate of water usage can then be calculated as:
\[ \text{Rate} = \frac{\text{Change in water used}}{\text{Change in time}} = \frac{30 \text{ gallons} - 0 \text{ gallons}}{6 \text{ minutes} - 0 \text{ minutes}} = \frac{30}{6} = 5 \text{ gallons per minute} \]
Now, we can evaluate the options provided:
A. The water usage is increasing at a rate of 5 gallons per minute. (This statement is correct based on the calculated rate.)
B. The water usage is increasing at a rate of per minute. (This statement is incomplete and thus cannot be evaluated as accurate.)
C. The water usage increases from 1 gallon to 2 gallons in 1 minute. (This statement is not supported by the information; the average rate is higher.)
D. The water usage increases from 1 gallon to 5 gallons in 5 minutes. (This statement is also not supported by the average rate calculation.)
Based on the analysis, the conclusion from the point (6, 30) on the graph is:
A. The water usage is increasing at a rate of 5 gallons per minute.