Question

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 divers depth. give your answer to the nearest hundredth. (1 point)
the quotient that describes the average rate of change for the diver’s depth is -0.99 meters/second.
the quotient that describes the average rate of change for the diver’s depth is -0.49 meters/second.
the quotient that describes the average rate of change for the diver’s depth is -3.47 meters/second.
the quotient that describes the average rate of change for the diver’s depth is 0.99 meters/second.

Explanation:

Step1: Identify the change in depth

The diver descends 10 meters. Since it's a descent (going lower), the change in depth $\Delta d=- 10$ meters.

Step2: Identify the time taken

The time taken for the descent $\Delta t = 10.1$ seconds.

Step3: Calculate the average rate of change

The average rate of change of depth (velocity in the vertical - direction) is given by the formula $v=\frac{\Delta d}{\Delta t}$. Substituting the values, we have $v=\frac{-10}{10.1}\approx - 0.99$ meters/second. The negative sign indicates that the depth is increasing (going downwards).

Answer:

The quotient that describes the average rate of change for the diver's depth is $-0.99$ meters/second.