Pop the champagne! At 7:46 ET Tuesday morning, the United States officially reached a population of 300 million. To understand why this is good news for investors, it's instructive to take a look back at history.

In 1915, when the population passed the 100 million threshold, the Dow Jones average fell just short of reaching 100 by the end of the year. In 1967, when the country reached the 200 million mark, the Dow had yet to crack to 1,000 barrier. Now it's hovering near an all-time record and could soon pass 12,000.

I mention all of this because it highlights the importance of long-term investing. The U.S. population is expected to reach the 400 million mark in 37 years, and if history is any guide, the stock market will continue to grow at a significantly faster rate than the population. The reason is simple: Businesses and workers alike have become ever more productive, and they're likely to continue to do so because of the accelerating rate of technological progress.

I will use history, again, to explain my optimism. In 2006, the cost of gas and milk were both cheaper, in inflation-adjusted terms, than in 1915. By 2043, is it not possible that many of today's existing products will similarly be cheaper?

One such product category that comes to mind is surgery -- often a costly, time-consuming process that can be performed only by a staff of highly trained and very specialized experts. In the future, companies such as Intuitive Surgical (NASDAQ:ISRG) could radically change the cost structure of such procedures and, in the process, save millions of people a lot of money.

Another example worth considering is automobiles. In 1915, only 2.5 million cars were on the road. Today, there are 237 million, and they have made many of us far more productive.

In 2006, there are about as many robots in operation as there were cars in 1915, and it's worth considering how many robots will be in operation by 2043. It's also worth thinking about how robot manufacturers like iRobot (NASDAQ:IRBT) might benefit from this growing trend. (I suppose it is also worth considering the possibility that these growing legions of robots could enslave us -- much as our automobiles have done to us with traffic jams.)

A third example to bear in mind is the treatment of disease. In 1915, one of the leading causes of death was tuberculosis. Today, that disease is quite rare. In all likelihood, society will witness comparable reductions in the death rate from many of today's leading diseases, such as HIV/AIDS, by the time the U.S. population reaches 400 million. New pharmaceutical advances from companies such as Gilead Sciences (NASDAQ:GILD), and an enhanced understanding of the human genome, as is being pursued at Genentech (NYSE:DNA), could fuel a revolution in health care.

Finally, it's instructive to note that when the U.S. reached a population of 200 million in 1967, life expectancy had just reached 70. Today, it is approaching 80. Companies poised to profit from these demographic changes, such as UnitedHealth Group (NYSE:UNH), could do quite well long into the future.

My broader point is that in spite of major wars and a decade-long economic depression, the United States has experienced both explosive population growth and unprecedented prosperity in the past eight decades. There are a lot of compelling reasons to believe that both trends will continue, and long-term investors should cheer today's 300 million milestone, because it suggests even greater progress yet to come.

Interested in more information about iRobot and Intuitive Surgical's future roles? Start up a 30-day free trial to Motley Fool Rule Breakers , where both stocks have been recommended, along with the stocks of other emerging technologies and potentially disruptive advancements.

UnitedHealth has been recommended in the Stock Advisor and Inside Value newsletter services.

Fool contributor Jack Uldrich is planning to be happily retired and playing with his yet-to-be born grandchildren when the U.S. reaches the 400 million mark in 2043. He owns stock in iRobot. The Fool has a strict disclosure policy.