Due to the tide, the water level rises and falls daily in Buzzard's Bay. D gives the depth of the water, in meters, t hours after midnight on a certain day. What is the best interpretation for the following statement? The value of the derivative of D at t=8 is equal to -0.5 . Choose 1 answer: (A) At 8 a.m. the water level decreased at a rate of 0.5 meters per hour. (B) At 8 a.m. the water level decreased at a rate of 0.5 meters. (C) At 8 a.m. the water level was 0.5 meters below sea level. (D) Until 8 a.m. the water level decreased at a rate of 0.5 meters per hour.

Question

Due to the tide, the water level rises and falls daily in Buzzard's Bay.  D gives the depth of the water, in meters,  t hours after midnight on a certain day. What is the best interpretation for the following statement? The value of the derivative of  D at  t=8 is equal to -0.5 . Choose 1 answer: (A) At 8 a.m. the water level decreased at a rate of 0.5 meters per hour. (B) At 8 a.m. the water level decreased at a rate of 0.5 meters. (C) At 8 a.m. the water level was 0.5 meters below sea level. (D) Until 8 a.m. the water level decreased at a rate of 0.5 meters per hour.

Bytelearn · Accepted Answer

Derivative Definition: The derivative of D with respect to t represents the rate of change of the water depth with respect to time.Derivative at t=8: At t=8, which is 8 a.m., the derivative is -0.5. This means the water level is changing at a rate of -0.5 meters per hour at that time.Negative Derivative: Since the derivative is negative, it indicates that the water level is decreasing, not increasing.Interpretation of Derivative at t=8: The correct interpretation of the derivative being -0.5 at t=8 is that at 8 a.m., the water level decreased at a rate of 0.5 meters per hour.

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