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.
The quotient that describes the rate of change in the squirrel’s height above the ground is 10.48 feet/second.
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Answer 1

To calculate the rate of change in the squirrel’s height above the ground, we start by determining the initial and final heights:

• Initial height of the squirrel (from the perch): 100 feet
• Final height of the squirrel (where the acorns are stored): 45 feet

Next, we calculate the change in height:

\[ \text{Change in height} = \text{Final height} - \text{Initial height} = 45 \text{ feet} - 100 \text{ feet} = -55 \text{ feet} \]

Now we divide this change by the time taken to move from the perch to the stored acorns to find the rate of change.

\[ \text{Rate of change} = \frac{\text{Change in height}}{\text{Time}} = \frac{-55 \text{ feet}}{5.25 \text{ seconds}} \approx -10.48 \text{ feet/second} \]

Thus, the interpretation of this quotient is:

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

So, the correct interpretation from the responses provided is:

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.