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): You can put this solution on YOUR website!
.
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?
~~~~~~~~~~~~~~~~~~~~~~~~

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.


    +------------------------------------------------------+
    |  This coefficient remains the same at every stroke.  |
    +------------------------------------------------------+


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  .

Solved.



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