If the rate of growth of industrial activity does not correlate with the warming why then is human activity being attributed to the cause of global warming?
The growth of industrialization is related to wealth created per investment. The investment and growth does not include the waste products. As technology grows, the industries that exhibit those technologies produce what they can vend and discard what is unusable. In the process of discarding what is unusable, other natural phenomena take place like; the CO2 output increases temperature slightly. That temperature increase melts out methane gas from tundra. Methane is a more potent greenhouse gas. Thus the rate of industrialization may reflect a linear growth while the global temperature exhibits a quadratic increase. The linear growth of industry is not correlated with the growth of global climate temperature.
Most natural phenomena are self regulating. There are linear feedback that regulate growth. If a population of grazing animals increases the numbers of predators increases and the population of grazing animals decreases. As the population of grazing animals decrease the population of predators also decreases. Thus the two populations regulate each other. If the ranching business (industry) sees predators as cutting into profit then predators are eliminated. Without predators the population of other non commercial grazers explodes without regulation. Because most natural systems involve more than one or two regulating conditions. Perhaps hundreds of actors involved in ecological regulation. Any human interference can be disastrous. So, research means that the case of climate change may be understood eliminating the controversy; what is the human factor?
In the case of global warming, human activity might be a small factor. I don't know. What I do know is that in the event that human activities are a primary cause and if life as we know it comes to an end the earth will continue as it has for 4 billion years. Continents will drift, ice ages will come and go, mountains will be pushed up and wear away, the earth will orbit the sun, and the sun will continue to burn its hydrogen. The people who panic and make demands are those who think they are critical to the great scheme of things. So, if we address what we can address we will have done what we can. If we continue to destroy our chances of long term survival (if that is what we are doing) then we only destroy ourselves. Who would miss us: the oceans; the mountains; the amoeba?