Question

A hot-air balloon was decommissioned after a successful flight by letting the 3000 m^3 of air in it leak out. The loss in the volume of air in the balloon was exponential, decreasing at x percent per minute. If there was 1626 m^3 of air in the balloon 15 minutes after it began to be decommissioned, at what percent per minute to the nearest percent did the balloon lose air?

A) 1%
B) 2%
C) 3%
D) 4%

Answer 1

for the first minute, the new volume of air is 3000 x
`(X)/(100)`because X% volume of air is lost every minute.What would've happened is a total of 3000 x
`((X)/(100))^(15)` would've been lost.

thus, what we have so far is:
3000 x
`((100 - X)/(100))^(15)` = 1626

`((100 - X)/(100))^(15)` =
`(1626)/(3000)`

`(100 - X)/(100) = \sqrt[15]{(1626)/(3000) }`


which is same as:

`(100 - X)/(100) = 0.95999` (rounded)

`100 - X = 0.95999` x 100
100 - X = 95.999
-X = 95.999 - 100
X ≈ 4

Therefore, 4% of air was lost from the balloon every minute.

BTW
The reason I did
`((X)/(100))^(15)` was because in multiplications, the order doesn't matter, so instead of doing

`(X)/(100)((X)/(100)((X)/(100)3000))....`
15 times, I just merged them into that equation

UPDATED sorry forgot some steps...