You drop a ball from a height of 1.5 meters. Each curved path has 75% of the height of the previous path. a. Write a rule for the sequence using centimeters. The initial height is given by the term n = 1. b. What height will the ball be at the top of the sixth path?
a. The rule for the sequence can be written as:
$h(n) = (0.75)^{n-1} \times 150$ cm
b. To find the height of the ball at the top of the sixth path, we substitute n = 6 into the rule:
$h(6) = (0.75)^{6-1} \times 150$ cm
$h(6) = (0.75)^5 \times 150$ cm
$h(6) = 0.2373 \times 150$ cm
$h(6) = 35.595$ cm
So, the ball will be at a height of 35.595 cm at the top of the sixth path.
wrong try again
I apologize for the mistake. Let's try again.
a. The rule for the sequence can be written as:
$h(n) = (0.75)^{n-1} \times 150$ cm
b. To find the height of the ball at the top of the sixth path, we substitute n = 6 into the rule:
$h(6) = (0.75)^{6-1} \times 150$ cm
$h(6) = (0.75)^5 \times 150$ cm
$h(6) = 0.2373 \times 150$ cm
$h(6) = 35.595$ cm
So, at the top of the sixth path, the ball will be at a height of 35.595 cm.