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 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 −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.

Answer 1

To find the rate of change in the squirrel's height above the ground, we first need to establish the change in height and the time taken.

1. Initial height of the squirrel: 100 feet
2. Final height (height of the acorns): 45 feet
3. Time taken: 5.25 seconds

Now, let's calculate the change in height:

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

Next, we can find the rate of change by dividing the change in height by the time taken:

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

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

Therefore, the correct response is:

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