SOLUTION: With each stroke, a pump removes 2/5 of the air in a container. After 3 strokes what is the fraction of the original amount of air in the container that is left?
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Question 1208622: With each stroke, a pump removes 2/5 of the air in a container. After 3 strokes what is the fraction of the original amount of air in the container that is left? Answer by ikleyn(52776) (Show Source):
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With each stroke, a pump removes 2/5 of the air in a container. After 3 strokes what is the fraction of the original amount
of air in the container that is left?
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Let M be the initial mass of the air in the container.
After first stroke, the remaining mass of the air in the container is = .
Thus we see that the coefficient from the current air mass to remaining mass
after the first stroke is 3/5.
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| This coefficient remains the same at every stroke. |
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After second stroke, the remaining mass of the air in the container is = .
After third stroke, the remaining mass of the air in the container is = = .
ANSWER. After third stroke, the remaining mass of the air in the container is .
The remaining fraction of the original mass is .
