Question
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The height that a property inflated basketball bounces decreases exponentially by with each subsequent bounce after the initial drop. A local
basketball league tests the inflation of their basketballs by dropping them from a height of 6 feet.
Which equation can be used to model the height of the basketball, , after bounces?
A.
B.
C.
D.

Ask by Bates Ward. in the United States
Jan 31,2025

Upstudy AI Solution

Tutor-Verified Answer

Answer

The correct equation to model the basketball’s height after bounces is .

Solution

To model the height of the basketball after each bounce, we can use an exponential decay function.
Here’s the step-by-step reasoning:
  1. Initial Height: The basketball is initially dropped from a height of 6 feet.
  2. Decay Rate: The height decreases by with each subsequent bounce. This means that after each bounce, the basketball retains of its previous height.
  3. Exponential Decay Formula:
    where:
    • is the height after bounces.
    • is the initial height (6 feet).
    • is the decay factor (0.722).
  4. Applying the Values:
Thus, the correct equation to model the height of the basketball after bounces is:
Answer:
B.

Answered by UpStudy AI and reviewed by a Professional Tutor

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Extra Insights

To model the height of the basketball after each bounce, we start by noting that the basketball retains of its height after each bounce, which is derived from . This means we can express the height as a function of the number of bounces. Therefore, the equation that best fits this scenario is .
To see how this applies in real life, let’s consider a player who wants to know how high their basketball will bounce after a series of free throws. If they drop the ball from 6 feet, they can quickly predict the bounce heights after each attempt, which helps in training and understanding the physics of the game. For example, after three bounces, the height can be calculated, giving them insight into what adjustments they might need to make for their shooting techniques!

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