A squirrel has stored its acorns in a hole that is 45 feet from the ground in a tall tree. The squirrel starts on a perch 100 feet above the ground. The squirrel moves from the perch down to its stored acorns in 5.25 seconds. Interpret the quotient to describe the rate of change in the squirrel’s height above the ground. Give your answer to the nearest hundredth.(1 point)

Question

Responses

The quotient that describes the rate of change in the squirrel’s height above the ground is −19.05 feet/second.
The quotient that describes the rate of change in the squirrel’s height above the ground is negative 19.05 feet/second.

The quotient that describes the rate of change in the squirrel’s height above the ground is 19.05 feet/second.
The quotient that describes the rate of change in the squirrel’s height above the ground is 19.05 feet/second.

The quotient that describes the rate of change in the squirrel’s height above the ground is −10.48 feet/second.
The quotient that describes the rate of change in the squirrel’s height above the ground is negative 10.48 feet/second.

The quotient that describes the rate of change in the squirrel’s height above the ground is 10.48 feet/second

Answer 1

To find the rate of change in the squirrel's height, we first determine the change in height and then divide by the time taken.

The squirrel starts at a height of 100 feet and moves down to a height of 45 feet. The change in height \( \Delta h \) is:

\[ \Delta h = \text{Final Height} - \text{Initial Height} = 45 \text{ feet} - 100 \text{ feet} = -55 \text{ feet} \]

Next, we divide this change by the time taken, which is 5.25 seconds:

\[ \text{Rate of change} = \frac{\Delta h}{\Delta t} = \frac{-55 \text{ feet}}{5.25 \text{ seconds}} \approx -10.48 \text{ feet/second} \]

Thus, the interpretation of the quotient is:

The quotient that describes the rate of change in the squirrel’s height above the ground is −10.48 feet/second.

Answer 2

A dolphin jumped above the surface of the water. It reached an altitude of 3.5 meters above the surface of the water and then dove 10 meters below the surface of the water. It went from its highest point above the water to its lowest depth in 12.5 seconds. Interpret the quotient to describe the average rate of change in the dolphin’s position. Give your answer to the nearest hundredth.(1 point)
Responses

The quotient that describes the rate of change in the dolphin’s position is 0.52 meters/second.
The quotient that describes the rate of change in the dolphin’s position is 0.52 meters/second.

The quotient that describes the rate of change in the dolphin’s position is −0.52 meters/second.
The quotient that describes the rate of change in the dolphin’s position is negative 0.52 meters/second.

The quotient that describes the rate of change in the dolphin’s position is −1.08 meters/second.
The quotient that describes the rate of change in the dolphin’s position is negative 1.08 meters/second.

The quotient that describes the rate of change in the dolphin’s position is 1.08 meters/second.
The quotient that describes the rate of change in the dolphin’s position is 1.08 meters/second.

Answer 3

To determine the average rate of change in the dolphin's position, we first need to calculate the change in position and then divide it by the time taken.

1. Calculate Change in Position:

   The dolphin reaches an altitude of 3.5 meters above the surface and then dives 10 meters below the surface. We can express these positions on a number line where the surface of the water is 0 meters:

   • The highest point above the water: \( +3.5 \) meters
   • The lowest point below the water: \( -10 \) meters

   The change in position \( \Delta p \) is calculated as follows: \[ \Delta p = \text{Final Position} - \text{Initial Position} = -10 \text{ meters} - 3.5 \text{ meters} = -13.5 \text{ meters} \]

2. Calculate the Time Taken: The time taken for this change is 12.5 seconds.

3. Calculate the Average Rate of Change: \[ \text{Average Rate of Change} = \frac{\Delta p}{\Delta t} = \frac{-13.5 \text{ meters}}{12.5 \text{ seconds}} \approx -1.08 \text{ meters/second} \]

Thus, the interpretation of the quotient is:

The quotient that describes the rate of change in the dolphin’s position is −1.08 meters/second.