It has been worked out... The relationship is linear. At any rate, the concern isn't the amount of heat absorbed, but the overall temperature, which is easily seen to be rising on the graphs.
And we must agree like any other medium, gas, solid, etc. that CO2 must surely have a saturation point where it simply cannot absorb more heat which would mean that CO2 has a maximum finite and measurable amount of heat that it can trap or absorb. If we assume that CO2 can absorb an infinite amount of heat then I would love to see that equation worked out on paper.