ShmoopTube

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Here's your shmoop du jour: brought to you by Grasshoppers. The insect, not the cookie.

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Although they both have a pretty nice crunch.

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A grasshopper jumps 1 foot to the right, then 1/2 the way back to the left.

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He then jumps another foot to the right, then 1/2 the way back.

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How far from his starting position will he be after 10 jumps?

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Round to the nearest hundredth of a foot.

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And here are the potential answers...

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Okay, so... he jumps 1 foot to the right, and then jumps halfway to his starting point.

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He ends up .5 feet away from his starting point after 2 jumps.

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He needs to keep track of his distance after 10 jumps, so we'll use a chart.

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So far, here is what we know:

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On his third jump, our insect friend will hop to the right again,

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and he'll increase his distance by 1 foot.

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Then, he'll jump backwards half the distance, and be .75 feet away after his 4th jump.

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We continue with his 5th and 6th jump, where he will jump to

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1.75 feet away, and return to be .875 feet away.

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On his 7th jump, he'll be 1.875 feet away, and half his distance to

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.9375 feet on his eighth. Finally, his last two jumps.

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He'll be 1.9375 feet away on his 9th jump,

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and .96875 feet away on his 10th and final jump.

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The question asks for the answer rounded to the hundredths place,

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so we round it off to .97 feet.

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So our answer is (A).

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