I'm looking to extrapolate rising temperatures based on the increasing CO2 levels. From this article: CO2 in 2050, with the following formula used to extrapolate the CO2 levels:
$CO_2\ level = 280 \cdot \left( 1+\exp(0.0222\cdot \left(year-2052\right)) \right)$. This formula gives the projected CO2 level in parts per million (ppm) for any year from 1958 on, assuming the growth rate is constant at 2.22%.
This seems fair since CO2 increases by 2.2% per year and it's effects are exponential.
I want to roughly use the same formula to extrapolate future temperatures based on this same CO2 increase as the accompanying document suggests: Temps using CO2. The issue is the constants used... because if the same formula is used, then at year 2052, the temperature would be doubled which is obviously not realistic.
So my question is: what coefficients should be used in this: $T=\left(1+\exp(ct)\right)$ formula, where $c$ is a constant ($0.0222$ I would think) and $t$ being a some measure of time.
Or is there a better formula to use which correlates exponentially increasing CO2 with increasing temperatures?