$12\mathrm{.}4$: Zeno's Memory Card

In $2016,128$ gigabytes $($GB$)$ of portable computer memory cost $$32.$

Here is a double number line that represents the situation:

mem

One set of tick marks has already been drawn to show the result of multiplying $128$ and $32$ each by $\frac{1}{2}.$ Label the amount of memory and the cost for these tick marks.

Next, keep multiplying by $\frac{1}{2}$ and drawing and labeling new tick marks, until you can no longer clearly label each new tick mark with a number.

$2.$ Here is a table that represents the situation. Find the cost of $1$ gigabyte. You can use as many rows as you need.

$3.$ Did you prefer the double number line or the table for solving this problem? Why?