Step-by-step explanation:
a.) To model this scenario
Let the height of ball = y
The height of 1st= 0.5y
2nd =0.5(0.5y)
3rd = 0.5*(0.5(0.5y))
Hence the height of nth bounce can be modeled as
Height of nth bounce =(0.5ⁿ-1)*y
The exponential equation is
hn= (0.5ⁿ-1)*y
b.) if the ball is dropped from 9ft above the ground
y= 9ft
On the 4th bounce
n=4
Substituting in the exponential equation we have
h4=(0.5^4-1)*9
h4=0.5³*9
h4= 0.125*9
h4= 1.125ft
On the 4th bounce, the ball will reach a height of 1.125ft
An exponential equation that gives the height [tex]n^{th}[/tex] ball will attain during the nth bounce is [tex]\frac{h}{2^{n} }[/tex].
On the 4th bounce, the ball will reach a height of [tex]\frac{9}{16}[/tex] feet.
Given:
The maximum height of each bounce will be one half of the height of the previous bounce
Let: The maximum height of the ball is h.
In the first bounce:
Maximum height = [tex]\frac{h}{2}[/tex]
In the second bounce:
Maximum height = [tex]\frac{h}{4}=\frac{h}{2^{2} }[/tex]
In the third bounce:
Maximum height = [tex]\frac{h}{8}=\frac{h}{2^{3} }[/tex]
in the [tex]n^{th}[/tex] bounce
Maximum height = [tex]\frac{h}{2^{n} }[/tex]
(a) [tex]\frac{h}{2^{n} }[/tex]
(b) h = 9 feet, n = 4
Maximum height = [tex]\frac{9}{2^{4} } =\frac{9}{16}[/tex] feet
Therefore, On the 4th bounce, the ball will reach a height of [tex]\frac{9}{16}[/tex] feet.
For more information:
https://brainly.com/question/23729449
