Over the past fifty years the carbon dioxide level in the atmosphere has increased. Carbon dioxide is believed to drive temperature, so predictions of future carbon dioxide levels are important. If C(t) is carbon dioxide level in parts per million (ppm) and t is time in years since 1950, three possible models are:
I C'(t) = 1.3
II C'(t) = 0.5 + 0.03t
III C'(t) = 0.5e^0.02t
(a) Given that the carbon dioxide level was 311 ppm in 1950, find C(t) for each model.
(b) Find the carbon dioxide level in 2020 predicted by each model.