Question

PLEASE HELP!!! I don't understand it

Answer 1

A

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

`y=a(b)^x`, or in our case:

`A(n)=a(b)^(n-1)`, 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,

`A(n)=1.5(.74)^(n-1)`

If ww want the height of the 6th bounce, n = 6. Filling that into the equation we already wrote for our model:

`A(6)=1.5(.74)^(6-1)` which of course simplifies to

`A(6)=1.5(.74)^5` which simplifies to

`A(6)=1.5(.22190066)`

So the height of the ball is that product.

A(6) = .33 cm

A is your answer