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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 −0.49 meters/second.
The quotient that describes the average rate of change for the diver’s depth is negative 0.49 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 −0.99 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 0.99 meters/second.
The quotient that describes the average rate of change for the diver’s depth is 0.99 meters/second.
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1 answer

To calculate the average rate of change in the diver's depth, we can use the formula for average rate of change:

\[ \text{Average Rate of Change} = \frac{\text{Change in Depth}}{\text{Time}}. \]

  1. Initial Depth: The diver starts at a depth of 15 meters below the surface, which can be represented as -15 meters.
  2. Final Depth: The diver descends to a depth of 10 meters lower than that, which is \(-15 - 10 = -25\) meters.
  3. Change in Depth: \[ \text{Change in Depth} = \text{Final Depth} - \text{Initial Depth} = -25 - (-15) = -25 + 15 = -10 \text{ meters}. \]
  4. Time Taken: The descent took 10.1 seconds.

Now we can substitute these values into our formula:

\[ \text{Average Rate of Change} = \frac{-10 \text{ meters}}{10.1 \text{ seconds}} \approx -0.99009901 \text{ meters/second}. \]

Rounding this to the nearest hundredth:

\(-0.99\) meters/second.

So, the correct response is:

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