[Apologies if this is in the wrong sub-forum as my maths knowledge is not much more than basic]

Here is a sequence of numbers, starting at 1 and then doubling at each step until 128 is reached. It would produce a nice curve if plotted on a graph.

I - 1

II - 2

III - 4

IV - 8

V - 16

VI - 32

VI - 64

VIII - 128

If I wanted to reduce the sequence of numbers from eight to five, while retaining the curve and keeping the first and final numbers of the sequence the same, how would I calculate this?

So compressing it like this:

I - 1

II - ?

III - ?

IV - ?

V - 128

Also, while I am here, how would one calculate stretching the sequence in the perpendicular direction? So keeping a sequence of eight numbers this time, with 1 remaining as 1 and the final number (VIII) being diminished from 128 to, for instance, 100 and the curve adjusting relative to it?

So like this:

I - 1

II - ?

III - ?

IV - ?

V - ?

VI - ?

VI - ?

VIII - 100

Thanks in advance.