Question

You drop a ball from a height of 1.5 meters. Each curved path has 74% of the height of the previous path.

a. Write a rule for the sequence using centimeters. The initial height is given by the is term n = 1.
b. What height will the ball be at the top of the sixth path?

1) A(n) = 1.5 • (0.74)^x-1; 0.33cm
2)A(n) = 0.74 • (1.5)^x-1; 5.62cm
3) A(n) = 150•(0.74)^x-1; 33.29cm
4) A(n) = 150 • (74) ^x-1; 332,850,993,600cm

Answer 1

`(a)\ A(n) = 150 * (0.74)^{n-1`

`(b)\ A(6) = 33.29cm`

Explanation:

Given

`a = 1.5` --- initial

`b = 74\%` --- rate

Solving (a): The rule of the sequence

First convert
`a = 1.5` to centimeters

`a = 1.5 * 100`

`a = 150`

The equation is then calculated using the following geometric progression formula

`A(n) = ab^(n-1)`

This gives:

`A(n) = 150 * (74\%)^(n-1)`

Express percentage as decimal

`A(n) = 150 * (0.74)^{n-1`

Solving (b): The height on the 6th path

This implies that:

`n = 6`

So, we have:

`A(6) = 150 * (0.74)^{6-1`

`A(6) = 150 * (0.74)^5`

`A(6) = 150 * 0.222`

`A(6) = 33.3cm`