You have touched on an important concideration, the numbers are multiplying perhaps at the same rate as Moore's Law or perhaps at a slower rate but something in parralell with the new information age:
Moore's law is the observation that, over the history of computing hardware, the number of transistors on integrated circuits doubles approximately every two years. The period often quoted as "18 months" is due to Intel executive David House, who predicted that period for a doubling in chip performance (being a combination of the effect of more transistors and their being faster). 
The law is named after Intel co-founder Gordon E. Moore, who described the trend in his 1965 paper.    The paper noted that the number of components in integrated circuits had doubled every year from the invention of the integrated circuit in 1958 until 1965 and predicted that the trend would continue "for at least ten years".  His prediction has proven to be uncannily accurate, in part because the law is now used in the semiconductor industry to guide long-term planning and to set targets for research and development. 
The capabilities of many digital electronic devices are strongly linked to Moore's law: processing speed, memory capacity, sensors and even the number and size of pixels in digital cameras.  All of these are improving at (roughly) exponential rates as well (see Other formulations and similar laws). This exponential improvement has dramatically enhanced the impact of digital electronics in nearly every segment of the world economy.  Moore's law describes a driving force of technological and social change in the late 20th and early 21st centuries.  
Although this trend has continued for more than half a century, Moore's law should be considered an observation or conjecture and not a physical or natural law. Sources in 2005 expected it to continue until at least 2015 or 2020. [note 1]  However, the 2010 update to the International Technology Roadmap for Semiconductors has growth slowing at the end of 2013,  after which time transistor counts and densities are to double only every three years.