Deanna works on her math homework for 6 hours. in the first hour, she finishes half of her homework. in each successive hour, she finishes half as much homework as she did in the previous hour. what fraction of the homework that deanna originally had does she not finish within six hours?

Explanation:

This table may help you to understand how the amount of homework remaining is calculated:

Hour     Starting amount of HW   Finished HW       Remaining HW

First                    x                             (1/2)x                     x - x/2 = x/2

Second              x/2                          (1/2)(x/2) = x/4      x/2 - x/4 = x/4

Third                  x/4                          (1/2)(x/4) = x/8      x/4 - x/8 = x/8

Fourth                x/8                          (1/2)(x/8)               x/8 - x/16 = x/16

Fifth                    x/16                        (1/2)(x/16)              x/16 - x/32 = x/32

Sixth                   x/32                       (1/2)(x/32)             x/32 - x/64 = x/64

Then, after six hours she has not finished 1/64 parts of her homework.

Since every hour half of the homework is done, you can calculate the amount of work remaining, also, as an exponential decay with decaying factor 1/2:

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