When a rubber ball is dropped it bounces back up to a height 34

Question

as high as its previous height. You drop this ball from a height of 16 feet and measure its height after each bounce.

Which formula represents a geometric sequence that describes the height of the ball after the number of bounces n
?

(1 point)
Responses

an=16(34)n−1
A sub n is equal to 16 times 3 fourths raised to the n minus 1 power

an=34(16)n−1
A sub n is equal to 3 fourths times 16 raised to the n minus 1 power

an=16+(34)n−1
A sub n is equal to 16 plus 3 fourths raised to the n minus 1 power

an=(n−1)(34)(16)

Answer 1

To represent the height of the ball after each bounce as a geometric sequence, we can use the following formula:

\[ a_n = a_1 \cdot r^{n-1} \]

where:

• \( a_n \) is the height after \( n \) bounces,
• \( a_1 \) is the initial height,
• \( r \) is the common ratio (the factor by which the height changes with each bounce),
• \( n \) is the number of bounces.

In this case:

• The initial height \( a_1 = 16 \) feet (the height from which the ball is dropped),
• The common ratio \( r = \frac{3}{4} \) (the ball bounces back to \( \frac{3}{4} \) of its previous height).

Plugging these values into the formula gives:

\[ a_n = 16 \left(\frac{3}{4}\right)^{n-1} \]

This matches the first option in your responses:

an = 16(3/4)^(n - 1)

So, the correct answer is:

A sub n is equal to 16 times 3 fourths raised to the n minus 1 power.