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 whales depth. Give your answer to the nearest hundredth

Answer 1

To find the rate of change in the whale's depth as it swims up towards the surface, we can use the formula for the rate of change, which is given by:

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

1. Initial Depth: The whale is currently at a depth of 15 meters below the surface, which can be expressed as -15 meters (since below the surface is negative).

2. Final Depth: When the whale reaches the surface, its depth is 0 meters.

3. Change in Depth: \[ \text{Change in Depth} = \text{Final Depth} - \text{Initial Depth} = 0 - (-15) = 15 \text{ meters} \]

4. Time Taken: The whale takes 9.5 seconds to reach the surface.

5. Rate of Change Calculation: \[ \text{Rate of Change} = \frac{15 \text{ meters}}{9.5 \text{ seconds}} \approx 1.57894736842 \text{ meters per second} \]

6. Rounding: When rounding to the nearest hundredth: \[ \text{Rate of Change} \approx 1.58 \text{ meters per second} \]

Thus, the quotient that best describes the rate of change in the whale's depth is 1.58 meters per second.