Question

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) 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 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 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 −10.48 feet/second.

Answer 1

To determine the rate of change in the squirrel's height above the ground, we first need to calculate the distance the squirrel travels and then divide that distance by the time it takes to travel that distance.

1. **Initial Height**: The squirrel starts at a perch that is 100 feet above the ground.
2. **Final Height**: The squirrel moves to a hole that is 45 feet above the ground.

3. **Distance Traveled**:
\[
\text{Distance} = \text{Initial Height} - \text{Final Height} = 100 \text{ feet} - 45 \text{ feet} = 55 \text{ feet}
\]

4. **Time Taken**: The squirrel takes 5.25 seconds to reach the hole.

5. **Rate of Change**:
\[
\text{Rate of Change} = \frac{\text{Distance}}{\text{Time}} = \frac{-55 \text{ feet}}{5.25 \text{ seconds}} \approx -10.48 \text{ feet/second}
\]
The negative sign indicates that the squirrel is descending.

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