Question

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 decent in 10.1 seconds. Interpret the quotient to describe the rate of change in the divers depth?

Answer 1

To interpret the rate of change in the diver's depth, we need to calculate the change in depth and divide it by the time taken to make that change.

1. **Initial Depth**: The diver was at a depth of 15 meters.
2. **Final Depth**: She descended to a depth of \(15 + 10 = 25\) meters.
3. **Change in Depth**: The change in depth is:
\[
\text{Change in depth} = \text{Final Depth} - \text{Initial Depth} = 25 \text{ meters} - 15 \text{ meters} = 10 \text{ meters}
\]
4. **Time Taken**: The time taken for the descent is 10.1 seconds.

5. **Rate of Change in Depth**: The rate of change in the diver’s depth can be calculated by taking the quotient of the change in depth and the time taken:
\[
\text{Rate of Change} = \frac{\text{Change in Depth}}{\text{Time}} = \frac{10 \text{ meters}}{10.1 \text{ seconds}} \approx 0.9901 \text{ meters per second}
\]

So, the interpretation of the quotient is that the diver descended at a rate of approximately **0.99 meters per second** during her descent.