Question

You drop a ball from a height of 1.5 meters. Each curved path has 71% of the height is the previous path.

Answer 1

a. write a rule for the sequence using centimeters. The initial height is given by term n = 1

For this case we have a sequence of the form:

$an = a0 * (r) ^ {(n-1)}$

Where

a0: initial height

r: rate of change

n: number of paths

On the other hand we have the following conversion:

1 meter = 100 centimeters

Therefore we have:

$(1.5) * (100) = 150 cm$

Thus, the general rule for the sequence in centimeters is:

$an = 150 * (0.71) ^ {(n-1)}$

Answer:

a rule for the sequence using centimeters is:

$an = 150 * (0.71) ^ {(n-1)}$

b. what height will the ball be at the top of the sixth path

For this case, we substitute the value of n = 6 in the equation obtained in part a.

We have then:

$a6 = 150 * (0.71) ^ {(6-1)}\\a6 = 27.06 cm$

Answer:

the height of the ball will be 27.06 at the top of the sixth path

Answer 2

The general form for a geometric series is:
an = a1 r^(n-1)

with a1 as 1.5
and r = 0.71

So,
a.
The rule for sequence is:
an = 1.5 (0.71)^(n - 1)

b.
After the sixth path, the height of the ball at the top is
a6 = 1.5 (0.71)^(6 - 1)
a6 = 0.27 m