How have computers changed from 1945 to 2007?
The earliest computers were huge machines - higher than a man - and took up a large amount of space in a specially air-conditioned room. Input was by way of punched cards and processing was slow.
Programmers tediously wrote their programs onto paper sheets then 'desk-checked' them in an attempt to ensure they were error free, before submitting them to the card punch operators. Because the computer resource was limited, programs were normally only assembled at night, so if a program contained even one error, there was usually a 24-hour turnaround to correct it.
The earliest computers were generally reserved for important research projects. Business accounting had to be performed by pen and paper, aided by slow manual calculators and adding machines.
We had already surpassed those computers by the 90s, and in 2007, the computer mentioned previously would have been considered inexcusably slow for its size. A laptop, costing far, far, far less, would have easily outperformed it, and with much less effort on the users part. In fact, nevermind 1945 - we have improved so much that a feature-phone from 2007 could outperform a desktop computer from the early 90s in RAM, storage capacity and processor output.
As you are likely aware, we do still have computers that fill entire rooms, however these are supercomputers, and are used for extremely intensive tasks. These can decrease the time a calculation takes 1000-fold.
Speculation: It is possible that today's supercomputers will be tomorrow's home computers, but without some drastic breakthrough, it will likely take half a century as it has done in the past.