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
