Question

To find the average rate of change in the diver's depth, we need to first determine the change in depth during the descent.

The diver started at a depth of 15 meters below the surface and descended to a depth that is 10 meters lower than that. This means she ended up at:

\[ 15 + 10 = 25 \text{ meters below the surface}. \]

So, the change in depth (\( \Delta d \)) is:

\[ \Delta d = 25 \text{ m} - 15 \text{ m} = 10 \text{ m}. \]

Next, we need to determine the time taken for this descent, which is given as 10.1 seconds.

The average rate of change of depth (\( R \)) can be calculated using the formula:

\[ R = \frac{\Delta d}{\Delta t}, \]

where \( \Delta d \) is the change in depth and \( \Delta t \) is the change in time.

Plugging in the values we have:

\[ R = \frac{10 \text{ m}}{10.1 \text{ s}} \approx 0.9901 \text{ m/s}. \]

Since the diver is going deeper (which is below the surface), we represent this rate as negative:

\[ R \approx -0.99 \text{ m/s} \text{ (to the nearest hundredth)}. \]

Therefore, the correct interpretation of the average rate of change for the diver's depth is:

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