How fast is the water running out of the swimming pool?
What is the function to calculate the gallons of water in the swimming pool over time?
The number of gallons of water in a swimming pool t minutes after the pool has started to drain is Q(t) = 50(20 - x)².
How fast is the water running out at the end of 11 minutes?
a. 4050 gal/min b. 2025 gal/min c. 450 gal/min d. 900 gal/min
Final answer:
In order to determine how fast the water is draining from the pool after 11 minutes, you calculate the derivative of the function Q(t) = 50(20 - t)² which ends up being -900 gallons per minute.
Answer:
The water is running out of the swimming pool at a rate of -900 gallons per minute at the end of 11 minutes.
The function Q(t) = 50(20 - t)² represents the number of gallons of water in the swimming pool at time t minutes after the pool has started to drain. To determine how fast the water is running out at the end of 11 minutes, we need to calculate the derivative of this function.
To find the derivative of Q(t), we use the chain rule and the power rule. After calculating the derivative, we substitute t = 11 into the derivative equation to find the rate at which the water is flowing out of the pool at that specific moment.
In this case, the derivative of Q(t) is Q\'(t) = -100(20 - t). Substituting t = 11, we get Q\'(11) = -900. Therefore, the water is running out at a rate of 900 gallons per minute at the end of 11 minutes.