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Question 1030499: 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? Thanks for the help!
Answer by stanbon(75887)   (Show Source):
You can put this solution on YOUR website! 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? Thanks for the help!
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Form:: y = a*b^x
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f(0) = 3000 = a
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f(15) = 3000*b^15 = 1626
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Solve for "b"::
b^15 = 1626/3000 = 0.542
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b = 0.542^(1/15) = 0.9599
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Note:: "b" is the survival percentage
The loss percentage is 1-0.9599 = 0.04 or 4%
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Cheers,
Stan H.
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