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. Is the answer negative, or positive?
To find the quotient, we divide the change in the diver's depth by the time it took to make that descent: \(\frac{10m}{10.1s} \approx 0.99 m/s\).
The quotient represents the rate of change in the diver's depth, which is approximately 0.99 meters per second.
Since the diver was descending, the depth change is negative, and therefore the answer is negative. So, the answer is -0.99.
To interpret the quotient describing the rate of change in the diver's depth, we need to calculate the average velocity. The average velocity can be found by dividing the change in depth by the time taken.
Change in depth = 15 meters (initial depth) - 10 meters (lower depth) = 5 meters
Time taken = 10.1 seconds
Average velocity = Change in depth / Time taken = 5 meters / 10.1 seconds
Simplifying the division, the average velocity is approximately 0.49 meters per second.
Since the diver descended from the initial depth to a lower depth, the rate of change is negative. Therefore, the answer is approximately -0.49 meters per second.