# A balloon filled with helium has a volume of 20,000 cm^3. The balloon loses 1/5 of its helium every 24 hours. What volume of the helium will be in the balloon at the start of the sixth day and then on the seventh day?

The volume at the start of the sixth day will be 6,553.6 cubic centimeters, while at the start of the seventh day the volume will be 5,242.88 cubic centimeters.

Let's translate the given information into mathematical language. "Loses 1/5 of its helium" means that the volume of helium V will become `V - 1 / 5 V = ( 1 - 1 / 5 ) V = 4 / 5 V ` after `24 ` hours.

This way, the remaining volume will be `4 / 5 ( 4 / 5 ) V = ( 4 / 5 ) ^ 2 V ` after one more 24-hour period, `( 4 / 5 ) ^ 3 V ` after one more, and so on.

"The start of the sixth day" means `5 ` times by `24 ` hours will pass, so the remaining volume will be `V_5 = ( 4 / 5 ) ^ 5 V_0 , ` where `V_0 ` is the given original volume.

Now we can give the answer in numbers. At the start of the fifth day, the remaining volume of helium will be

`( 4 / 5 ) ^ 5 * 20,000 = 6,553.6 ( cm ^ 3 ) .`

To find the remaining volume after `n ` days, we use the formula `V ( n ) = ( 4 / 5 ) ^ n V_0 . ` For the start of the seventh day, use `n = 6 , ` which will give `5,242.8 8 cm ^ 3 .`

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