A bouncing ball is dropped from a height of 200 cm.The ball loses 30% of it's height on every bounce. write the equation that will give the height of the ball at the top of each bounce.use h for the height of the ball,and n for the number of each bounce.

- stapel_eliz
**Posts:**1686**Joined:**Mon Dec 08, 2008 4:22 pm-
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To figure out the equation, start doing the computations for the first few bounces.

When there had been zero bounces (that is, when the ball hadn't been dropped yet), the height h was 200.

Since thirty percent of this height was lost on the first bounce, then the first bounce reached only seventy percent of the first height. What then was the height after x = 1 bounces?

After the second bounce, the ball reached only seventy percent of the height after the first bounce. What was the height h after x = 2 bounces?

And so forth, until you notice the pattern, and create the formula.

When there had been zero bounces (that is, when the ball hadn't been dropped yet), the height h was 200.

Since thirty percent of this height was lost on the first bounce, then the first bounce reached only seventy percent of the first height. What then was the height after x = 1 bounces?

After the second bounce, the ball reached only seventy percent of the height after the first bounce. What was the height h after x = 2 bounces?

And so forth, until you notice the pattern, and create the formula.

- maggiemagnet
**Posts:**348**Joined:**Mon Dec 08, 2008 12:32 am-
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It's really helpful to not actually do the arithmetic as you go, because you can see what's happening better.

x=0: 200

x=1: 0.7*200

x=2: 0.7(0.7*200) = 0.7^2*200

x=3: 0.7(0.7^2*200) = 0.7^3*200

See?

x=0: 200

x=1: 0.7*200

x=2: 0.7(0.7*200) = 0.7^2*200

x=3: 0.7(0.7^2*200) = 0.7^3*200

See?