A ball bounces .6 of its height on every bounce. If a ball us dropped from 200 feet, how high does it bounce on the fifth bounce? Round to the nearest tenth.

To determine how high the ball bounces on the fifth bounce, we can model this as a geometric sequence.

Each bounce is 0.6 (60%) of the previous height, and the ball starts at 200 feet. The general formula for the height after \( n \) bounces is:

\[
h_n = h_0 \times r^n
\]
where:
- \( h_0 \) is the initial height (200 feet),
- \( r \) is the ratio of each bounce (0.6),
- \( n \) is the number of bounces.

For the fifth bounce (\( n = 5 \)):

\[
h_5 = 200 \times 0.6^5
\]

Let's calculate that.

\[
h_5 = 200 \times 0.6^5 = 200 \times 0.07776 = 15.552
\]

Rounded to the nearest tenth, the height on the fifth bounce is **15.6 feet**.

Do you want further details or have any questions?

Here are 5 related questions for practice:
1. How high will the ball bounce after the third bounce?
2. What is the total distance the ball has traveled by the fifth bounce?
3. How many bounces are needed for the ball to bounce less than 1 foot?
4. What if the ball retained 70% of its height on each bounce instead of 60%?
5. How high would the ball bounce after 10 bounces?

**Tip:** Geometric sequences are often used to model repeated processes where a fixed percentage is lost or gained each time!

A ball bounces 0.6 of its height on every bounce. If a ball is dropped from 200 feet, how high does it bounce on the fifth bounce? Round to the nearest tenth.

Learn how to calculate the height of a bouncing ball using a geometric sequence. This problem demonstrates how a ball dropped from 200 feet bounces 0.6 of its height on each bounce, and how to calculate the height on the fifth bounce. Suitable for students in Grades 8-10.

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