To find the rate of change of the whale's depth as it swims up towards the surface, we can use the following formula:
\[ \text{Rate of Change} = \frac{\text{Change in Depth}}{\text{Time}} \]
The whale starts at a depth of 15 meters (below the surface), which we consider as -15 meters, and swims up to the surface, which is 0 meters. Therefore, the change in depth can be calculated as:
\[ \text{Change in Depth} = \text{Final Depth} - \text{Initial Depth} = 0 - (-15) = 15 , \text{m} \]
The time taken to swim to the surface is 9.5 seconds.
Now we calculate the rate of change:
\[ \text{Rate of Change} = \frac{15 , \text{m}}{9.5 , \text{s}} \approx 1.5789 , \text{m/s} \]
To find the answer to the nearest hundredth, we round 1.5789 to:
\[ \text{Rate of Change} \approx 1.58 , \text{m/s} \]
Thus, the quotient that best describes the rate of change in the whale's depth is approximately 1.58 meters per second.
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