Question

A golf ball is manufactured so that if it is dropped from A feet above the ground onto a hard surface, the maximum height of each bounce will be one half of the height of the previous bounce.

Find an exponential equation that gives the height h the ball will attain during the nth bounce.

If the ball is dropped from 14 feet above the ground onto hard a surface, how high will it bounce on the 6th bounce?
On the 6th bounce, the ball will reach a height of
feet.

Answer 1

The height \( h \) of the ball during the \( n \)th bounce can be described by an exponential equation of the form:

\[ h_n = A \left( \frac{1}{2} \right)^n \]

where:

- \( A \) is the initial height of the ball on the first bounce.

In this case, you mentioned that the ball is dropped from 14 feet above the ground, so the initial height \( A \) is 14.

Therefore, the equation representing the height of the ball during the \( n \)th bounce is:

\[ h_n = 14 \left( \frac{1}{2} \right)^n \]

To find the height of the ball on the 6th bounce (\( n = 6 \)), substitute \( n = 6 \) into the equation:

\[ h_6 = 14 \left( \frac{1}{2} \right)^6 \]

Now, calculate \( h_6 \) to find the height on the 6th bounce.