A scuba diver was at a depth of 15 meters below the surface when she saw something interesting about 10 meters lower. She made the descent in 10.1 seconds. Interpret the quotient to describe the rate of change in the diver’s depth. Give your answer to the nearest hundredth.

Answer 1

To find the rate of change in the diver's depth, we first need to determine the total change in depth that the diver experienced and then divide that by the time it took for the descent.

1. The diver started at a depth of 15 meters.
2. She descended to 10 meters lower, which means her final depth is \(15 + 10 = 25\) meters.

Now, we can calculate the change in depth:

\[ \text{Change in depth} = \text{final depth} - \text{initial depth} = 25 , \text{meters} - 15 , \text{meters} = 10 , \text{meters} \]

Next, we divide the change in depth by the time taken to find the rate of change:

\[ \text{Rate of change} = \frac{\text{Change in depth}}{\text{Time}} = \frac{10 , \text{meters}}{10.1 , \text{seconds}} \approx 0.990099 , \text{meters per second} \]

To express this rate to the nearest hundredth:

\[ \text{Rate of change} \approx 0.99 , \text{meters per second} \]

Thus, the rate of change in the diver's depth is approximately 0.99 meters per second.