A fan is running at 10 revolutions per second. After it is turned off, it's speed decreases at a rate of 75% per second. Determine the number of revolutions completed by the fan after it is turned off.

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A fan is running at 10 revolutions per second. After it is turned off, it's speed decreases at a rate of 75% per second. Determine the number of revolutions completed by the fan after it is turned off.

Mathematics
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what sequence do you think we should apply?
Infinite Geometric?
sounds good to me, and how to apply it?

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Other answers:

\[S \infty = \frac{ a }{ 1 - r }\]
r = .75 a = first term = 10
I was wondering it that was the correct approach and answer? Or do I use a different formula?
i dont think r=.75, i could be mistaken tho if it decreases at a rate of k, then it retains 1-k of its speed, right?
Yes
So if it decreases .75, then it retains .25
10 + 10(.25) + 10(.25)(.25) + ...
so 40/3 sounds fair
How did you get that though, 40/3?
10/(1-.25) = 10/(3/4) = 10*4/3
Ah
R is the common ratio, so r = .25?
i would say so. we want to determine how much of the rotations we are retaining. in order to count them.
This type of problem just happened to be the one I got incorrect on my exam. Thank you for your help!
accursed exams!! good luck :)
Thank you! :D

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