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A scuba diver was at a depth of 15 meters below the surface when she saw something interesting about 10 meters lower. She made the descent in 10.1 seconds. Interpret the quotient to describe the rate of change in the diver’s depth. Give your answer to the nearest hundredth.(1 point)

Responses

The quotient that describes the average rate of change for the diver’s depth is 0.99 meters/second.
The quotient that describes the average rate of change for the diver’s depth is 0.99 meters/second.

The quotient that describes the average rate of change for the diver’s depth is −0.99 meters/second.
The quotient that describes the average rate of change for the diver’s depth is negative 0.99 meters/second.

The quotient that describes the average rate of change for the diver’s depth is −3.47 meters/second.
The quotient that describes the average rate of change for the diver’s depth is negative 3.47 meters/second.

The quotient that describes the average rate of change for the diver’s depth is −0.49 meters/second.

1 answer

To find the average rate of change of the diver's depth, we need to determine the change in depth and divide it by the time taken for that change.

  1. Initial depth: The diver starts at 15 meters below the surface, which we can represent as -15 meters.
  2. Final depth: The diver descends to a depth that is 10 meters lower than her starting depth: \[ \text{Final depth} = -15 , \text{meters} - 10 , \text{meters} = -25 , \text{meters} \]
  3. Change in depth: \[ \text{Change in depth} = \text{Final depth} - \text{Initial depth} = -25 , \text{meters} - (-15 , \text{meters}) = -25 + 15 = -10 , \text{meters} \]
  4. Time taken: The diver took 10.1 seconds to make this descent.
  5. Average rate of change: \[ \text{Average rate of change} = \frac{\text{Change in depth}}{\text{Time}} = \frac{-10 , \text{meters}}{10.1 , \text{seconds}} \approx -0.9901 , \text{meters/second} \]

Rounding this to the nearest hundredth, we get: \[ -0.99 , \text{meters/second} \]

The correct response is: The quotient that describes the average rate of change for the diver’s depth is −0.99 meters/second.