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Question 1

A)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 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.
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 19.05 feet/second.

1 answer

To determine the rate of change in the squirrel's height above the ground, we can use the formula for the rate of change, which is the change in height divided by the time taken.

First, we need to calculate the change in height:

  • The initial height of the squirrel when it starts on the perch is 100 feet.
  • The height of the squirrel when it reaches the acorns is 45 feet.

The change in height = initial height - final height = 100 feet - 45 feet = 55 feet.

Now, we need to find the rate of change of height over the time taken. The time taken for the squirrel to move down is 5.25 seconds.

Rate of change = change in height / time = 55 feet / 5.25 seconds ≈ 10.48 feet/second.

Since the squirrel is moving down, we can express this rate as negative, indicating a decrease in height:

Thus, 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.