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. To write a rule for the sequence using centimeters, we know that the initial height is 1.5 meters, which is equivalent to 150 centimeters. Each curved path has 75% of the height of the previous path. Therefore, the rule for the sequence is:
Height(n) = 0.75 * Height(n-1)
B. To find the height at the top of the sixth path, we can use the rule from part A. We know that the initial height is 150 centimeters, so we can calculate the height at the top of the sixth path as:
Height(6) = 0.75 * Height(5)
Using the rule repeatedly:
Height(6) = 0.75 * (0.75 * (0.75 * (0.75 * (0.75 * 150))))
Height(6) = 0.75^5 * 150
Height(6) ≈ 78.515625 * 150
Height(6) ≈ 117.77 centimeters
Therefore, the height at the top of the sixth path would be approximately 117.77 centimeters.