Final answer:
To find the time when the instantaneous rate of water draining from the tank is 1,000 gallons/minute, you need to determine when the slope of the graph of the water level versus time is equal to 1,000 gallons/minute.
Step-by-step explanation:
The question asks at what time the instantaneous rate of the water draining from the tank is 1,000 gallons/minute. To find this time, you need to determine when the rate of change of water in the tank is equal to 1,000 gallons/minute. This can be determined by finding the time when the slope of the graph of the water level versus time is equal to 1,000 gallons/minute.
You can use the concept of the derivative to find the slope of the graph at different time intervals. When the slope is equal to 1,000 gallons/minute, that is the time when the water is draining from the tank at a rate of 1,000 gallons/minute.
Based on the given information, none of the options (t = 11 minutes, t = 8 minutes, t = 10 minutes, t = 12 minutes, t = 9 minutes) can be determined as the time when the instantaneous rate of water drainage is 1,000 gallons/minute.