Straight line, it's just over 51% increase each generation for five generations. It didn't happen like this of course, there were leaner times and times of massively increased prosperity, albeit relative to a very low start point.
The Industrial Revolution did not really impact until towards the end of this period. You are more likely to find the reasons in better health care (medical advances of the time and their availability), more efficient farming and availability of food in bad times.
Ironic given, what happened in 47 and 48 and the Liberal Whig dogma on free markets that lead to 12.5% starving to death and another 12.5% leaving the country. The Tories of the time incidentally, would have pursued policies that would have alleviated the suffering of the famine.
This isn't really my area of history. I'm just an O'connell fan.
Well much of those efficiencies and medical and scientific advances are strictly speaking part of the first phase of the Industrial Revolution which took place in the 18th century. But I take your point.
As to what the Tories might or might not have done with regard to the Famine, we'll never really know that for sure. Though you may be right.
While the Famine was driven by economic factors, it's worth remembering that the economics were also driven by ethnic and sectarian factors, and that when it came to alleviation of the Famine sectarianism played a huge factor.
The term "Soupers" came in to use during the famine, because soup kitchens would only give food to the Protestant starving in many areas, conversion rates went up in those areas as families of Roman Catholics adopted Protestantism to avoid starvation.
Some Protestants (admittedly usually older ones) still make the distinction between old Protestant families and Soupers when talking about other Protestants. It doesn't mean anything these days, but it did mean something very potent for a long time and did so until relatively recently.