In the past 50 to 100 years, man has burned about one halve of all the oil which formed through the ages, plus large amounts of coal, lumber, and natural gas. This is the source of the carbon dioxide. It would be worse except the oceans absorbed some of the carbon dioxide increase.
Initially in an instance. Following the best evidence supported theory, the Universe came into existence suddenly with the big bang, some 13.7 billion years ago. The Universe is STILL forming as it expands and ages.
Either. You could have carbon isotope ratios as your independent and carbon age as your dependent. or You could have the carbon age of soil samples as your independent and the artefacts that you are trying to date as the dependent.