A whale is swimming at a current depth of 15 meters below the surface. It swims up toward the surface and arrives there 9.5 seconds later. Find the quotient that best describes the rate of change in the whale’s depth. Give your answer to the nearest hundredth.(1 point)

Answer 1

To find the rate of change in the whale's depth as it swims from 15 meters below the surface (a depth of -15 meters in a vertical coordinate system where the surface is 0) back to the surface (0 meters), we can use the following formula for the rate of change:

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

1. Change in Depth: The initial depth of the whale is -15 meters, and it rises to 0 meters at the surface. Thus, the change in depth is:

   \[ \text{Change in Depth} = \text{final depth} - \text{initial depth} = 0 - (-15) = 15 \text{ meters} \]

2. Time: The time taken to reach the surface is 9.5 seconds.

3. Calculating the Rate of Change:

   \[ \text{Rate of Change} = \frac{15 \text{ meters}}{9.5 \text{ seconds}} \approx 1.57894737 \text{ meters/second} \]

4. Rounding to the Nearest Hundredth: Rounding 1.57894737 to the nearest hundredth gives:

   \[ 1.58 \text{ meters/second} \]

Therefore, the quotient that best describes the rate of change in the whale’s depth is 1.58 meters/second.