MATHEMATICS HIGH SCHOOL

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%

Answers

Answer 1
Answer: 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...

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Answers

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Answer:

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