(maybe a good Friday afternoon task...)

1

2

4

8

16

32

...

this is the way that cells replicate

students may notice that the differences in powers of 2 are, again, powers of 2

if you jump two spaces the differences are always multiples of ?

if you jump three spaces the differences are always multiples of ?

graphing the function is a little awkward but it can be a helpful way of students appreciating the speed of growth:

students could think of the function in monetary terms: if your money doubled every year (i.e. 100% increase per annum) how long would it take for you to become a millionaire?

the numbers of digits in the powers of 2 seems to follow a pattern:

you get 4 of them with a length (3n - 2)

then 3 with a length (3n - 1) and

then 3 with a length (3n)

so to work out how many digits there are in a particular power of 2: you divide the whole number part of the power by 10, multiply this by 3 and

add 1 if the power ends in 0, 1, 2 or 3

add 2 if the power ends in 4, 5 or 6

add 3 if it ends in 7, 8 or 9

to check this, a pebibyte is 2 ^ 50 = 1125899906337504

50 divided by 10 is 5

5 x 3 is 15

add 1 is 16

this is the number of digits in the result

the lead digits seem to follow a similar 'block' pattern: 1 2 4 8 then 1 3 6 then 1 2 5

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