A tank is being filled with a liquid. The function V gives the volume of liquid in the tank, in liters, after t minutes.What is the best interpretation for the following statement?The value of the derivative of V at t=1 is equal to 2 .Choose 1 answer:(A) After 1 minute, the tank was being filled at a rate of 2 liters.(B) After 1 minute, the tank had 2 liters of liquid.(C) After 1 minute, the tank was being filled at a rate of 2 liters per minute.(D) During the first minute, the tank was being filled at a rate of 2 liters per minute.
Q. A tank is being filled with a liquid. The function V gives the volume of liquid in the tank, in liters, after t minutes.What is the best interpretation for the following statement?The value of the derivative of V at t=1 is equal to 2 .Choose 1 answer:(A) After 1 minute, the tank was being filled at a rate of 2 liters.(B) After 1 minute, the tank had 2 liters of liquid.(C) After 1 minute, the tank was being filled at a rate of 2 liters per minute.(D) During the first minute, the tank was being filled at a rate of 2 liters per minute.
Interpretation of Derivative: The derivative of V with respect to t represents the rate of change of the volume with respect to time. So, the derivative of V at t=1 being equal to 2 means that at t=1, the rate at which the volume is changing is 2 liters per unit of time.
Rate Calculation: Since the unit of time given in the problem is minutes, the rate of 2 liters per unit of time at t=1 translates to 2 liters per minute.
Matching with Choices: Now, we need to match this interpretation with the given choices. Choice (A) says "After 1 minute, the tank was being filled at a rate of 2 liters," which is incomplete because it doesn't specify the time frame for the rate. Choice (B) says "After 1 minute, the tank had 2 liters of liquid," which is incorrect because it describes the volume, not the rate. Choice (C) says "After 1 minute, the tank was being filled at a rate of 2 liters per minute," which correctly describes the rate of change of volume at t=1. Choice (D) says "During the first minute, the tank was being filled at a rate of 2 liters per minute," which is incorrect because it describes the average rate over the first minute, not the specific rate at t=1.
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