Question 3

A)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.(1 point)
Responses

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 negative 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 negative 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 negative 3.47 meters/second.

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

1 answer

To find the average rate of change in the diver's depth during her descent, we can use the formula for average rate of change:

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

The diver starts at a depth of 15 meters below the surface and descends to a depth of 25 meters (15 meters + 10 meters). Therefore, her change in depth is:

\[ \text{Change in Depth} = -25 - (-15) = -25 + 15 = -10 \text{ meters} \]

(The negative sign indicates that she is descending deeper into the water.)

The time taken for this descent is 10.1 seconds.

Now, substituting these values into the average rate of change formula:

\[ \text{Average Rate of Change} = \frac{-10 \text{ meters}}{10.1 \text{ seconds}} \approx -0.99 \text{ meters/second} \]

So, the quotient that describes the average rate of change for the diver’s depth is approximately -0.99 meters/second.

Thus, the correct response is:

The quotient that describes the average rate of change for the diver’s depth is −0.99 meters/second.