Stumped again .. A ball was dropped and measured rebound heights (in ft.) after each bounce. It was found that the rule y= 15(0.80^x) could be used to predict the rebound height of the ball, where y is the bounce height and x is the bounce number.

From what initial height did they drop the ball?
I come up with two different answers, 12 and 15 .. not sure which is correct, if either is even correct. ... i multiplied by 15 X .8 = 12 .. would this be correct?

Next, how do i figure how the rebound height changes from one bounce to the next?

Thanks again, in advance. - English is my forte`; obviously NOT algebra! lol

To find the initial height from which the ball was dropped, you can use the equation provided. In the equation y = 15(0.80^x), y represents the rebound height and x represents the bounce number.

Since the initial height is the height of the first bounce (x = 0), you can substitute x = 0 into the equation and solve for y.

y = 15(0.80^0)
y = 15(1)
y = 15

Therefore, the initial height from which the ball was dropped is 15 feet.

To determine how the rebound height changes from one bounce to the next, you need to find the difference between the rebound heights of consecutive bounces.

Let's say you want to find the change in rebound height from the first bounce (x = 1) to the second bounce (x = 2).

Substitute x = 1 into the equation to find the rebound height after the first bounce:
y1 = 15(0.80^1) = 12

Then substitute x = 2 into the equation to find the rebound height after the second bounce:
y2 = 15(0.80^2) = 9.6

To find the change in rebound height, subtract the rebound height after the first bounce from the rebound height after the second bounce:
Δy = y2 - y1 = 9.6 - 12 = -2.4

In this case, the rebound height decreased by 2.4 feet from the first bounce to the second bounce.

Repeat this process for any two consecutive bounces to determine how the rebound height changes from one bounce to the next.

To find the initial height from which the ball was dropped, you need to examine the equation given. In this case, the equation is y = 15(0.80^x), where y represents the bounce height and x represents the bounce number. When the ball is first dropped (x = 0), the height of the bounce should be equal to the initial height from which it was dropped.

Substituting x = 0 into the equation, we get:

y = 15(0.80^0)
y = 15(1)
y = 15

Therefore, the initial height from which the ball was dropped is 15 feet. Your second answer, 12 feet, is incorrect.

To determine how the rebound height changes from one bounce to the next, you can calculate the difference in height between consecutive bounces. Let's say you want to find the change in height from the first bounce to the second bounce.

Substitute x = 1 and x = 2 into the equation:

For first bounce (x = 1):
y1 = 15(0.80^1)
y1 = 15(0.80)
y1 = 12

For second bounce (x = 2):
y2 = 15(0.80^2)
y2 = 15(0.64)
y2 = 9.6

The change in height from the first to the second bounce is:

Change in height = y2 - y1
Change in height = 9.6 - 12
Change in height = -2.4

So, the rebound height decreases by 2.4 feet from the first to the second bounce.

You can use a similar process to find the change in height between any two consecutive bounces.