Question

A bouncy ball is dropped. The function h(n) = 300(3/4)^n-1 models the maximum height of the ball, in centimeters, after its nth bounce. Select EACH true statement about the scenario.

The function represents a geometric sequence.
The first term in the sequence is 300.
The height of the ball after the first bounce is 300 cm.
The ball is dropped from a height of 300 cm.
a) 1) True 2) True 3) True 4) True
b) 1) True 2) True 3) True 4) False
c) 1) True 2) True 3) False 4) True
d) 1) True 2) True 3) False 4) False

Answer 1

The first statement is true, the second statement is true, and the third statement is false.

Step-by-step explanation:

The statement 'The first term in the sequence is 300' is true. The first bounce is considered the first term of the sequence, and the height of the ball after the first bounce is indeed 300 cm. However, the statement 'The ball is dropped from a height of 300 cm' is false. The ball is not dropped from a height of 300 cm; instead, the function represents the maximum height of the ball after each bounce.

To determine whether the function represents a geometric sequence, we need to check if there is a common ratio between consecutive terms. In this case, the common ratio is 3/4, so the function does represent a geometric sequence.