Answer:
A
Step-by-step explanation:
This is exponential decay; the height of the ball is decreasing exponentially with each successive drop. It's not going down at a steady rate. If it was, this would be linear. But gravity doesn't work on things that way. If the ball was thrown up into the air, it would be parabolic; if the ball is dropped, the bounces are exponentially dropping in height. The form of this equation is
[tex]y=a(b)^x[/tex], or in our case:
[tex]A(n)=a(b)^{n-1}[/tex], where
a is the initial height of the ball and
b is the decimal amount the bounce decreases each time. For us:
a = 1.5 and
b = .74
Filling in,
[tex]A(n)=1.5(.74)^{n-1}[/tex]
If ww want the height of the 6th bounce, n = 6. Filling that into the equation we already wrote for our model:
[tex]A(6)=1.5(.74)^{6-1}[/tex] which of course simplifies to
[tex]A(6)=1.5(.74)^5[/tex] which simplifies to
[tex]A(6)=1.5(.22190066)[/tex]
So the height of the ball is that product.
A(6) = .33 cm
A is your answer
