A bunny hops across a garden to a fence at the end. First he hops half the distance and then as he gets tired he hops half the distance that remains. If the width of the garden is 1024cm, how many hops (incl the first) does the bunny need to make before he is 1cm from the other side?
Can you Please please show your workings out. Thank you so much!
Image by Ahmed Rabea
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the question is missing something,
how far is the distance of one hop of the bunny?
Well, before the first hop (time t=0) he has 1024cm left to go. On the first hop(time t=1), he has 512cm to go. This can be modeled by y = 1024/2^t. We need to know when y is less than 1cm.
That is:
1024 / 2^x < 1
1024 < 2^x
2^10 < 2^x
x > 10
So the rabbit will be getting there after 11 hops.
since the bunny hops half the distance everytime, we can solve this using binary principle…
1024 is 2^11 …. therefore, before the bunny is 1cm from the other side, ready to make his last hop, he should have made already 10 hops …
have a nice day …