To find the average rate of change in the diver's depth during her descent, we can use the formula for average rate of change:
\[ \text{Average Rate of Change} = \frac{\text{Change in Depth}}{\text{Change in Time}} \]
The diver starts at a depth of 15 meters below the surface and descends to a depth of 25 meters (15 meters + 10 meters). Therefore, her change in depth is:
\[ \text{Change in Depth} = -25 - (-15) = -25 + 15 = -10 \text{ meters} \]
(The negative sign indicates that she is descending deeper into the water.)
The time taken for this descent is 10.1 seconds.
Now, substituting these values into the average rate of change formula:
\[ \text{Average Rate of Change} = \frac{-10 \text{ meters}}{10.1 \text{ seconds}} \approx -0.99 \text{ meters/second} \]
So, the quotient that describes the average rate of change for the diver’s depth is approximately -0.99 meters/second.
Thus, the correct response is:
The quotient that describes the average rate of change for the diver’s depth is −0.99 meters/second.