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# Some help on a interesting question (functions)

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I am pushing my friend on a swing, every time that it swings back and forth the amount it swings decreases by 30%. The first time I pushed my friend the swing traveled 12 feet. How many times will it take for the distance that they travel to turn into 0?

Note: This is an interesting question since I know the exponential function is equal to 12 x (0.7) ^ (x-1)

I think that it can't get to 0 but I do know that swings do stay still.

Am I considering this problem to deeply?

Thanks!

Sep 15, 2023

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It will  (theoretically) travel

12 / ( 1 - .7)  =   12 / (3/10) =  (12 * 10) / 3  =   40 ft

However....if we set the sum of an infinite geometric series to 40

12 [ 1 - .7^r ] / [ 1 - .7 ]   =  40

12 [ 1 - .7^r ] / .3  = 40

12 [ 1 - .7^r ] =  12

1 - .7^r  =  1

-.7^r  = 0

Which means that the number of times  (r) that it takes to get the swing to  stop is not determinable......however, with friction involved it will eventually stop

Sep 16, 2023