Question

Question
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)
The quotient that best represents the rate of change in the whale’s depth is

Answer 1

To find the rate of change in the whale's depth, we can use the formula for rate of change, which is:

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

1. **Determine the change in depth**:
- The whale starts at a depth of 15 meters (which is below the surface, so we can use -15 meters).
- It swims up to the surface, which is 0 meters.
- Therefore, the change in depth is:

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

2. **Determine the time**:
- The time taken for this change is 9.5 seconds.

3. **Calculate the rate of change**:
\[
\text{Rate of Change} = \frac{\text{Change in Depth}}{\text{Time}} = \frac{15 \text{ meters}}{9.5 \text{ seconds}}
\]

Now we compute the quotient:

\[
\text{Rate of Change} = \frac{15}{9.5} \approx 1.5789
\]

4. **Round to the nearest hundredth**:
\[
1.5789 \approx 1.58
\]

Thus, the quotient that best represents the rate of change in the whale’s depth is **1.58** meters per second.