Final answer:
The function that best models the CO₂ concentration above 250 ppm I years after 1850 is likely to be an exponential function due to the accelerating increase of CO₂ levels, especially in recent decades, as indicated by historical data from ice cores and atmospheric measurements.
Step-by-step explanation:
To determine the function that best models y, the CO₂ concentration above 250 ppm I years after 1850, it's essential to look at the historical data and the pattern of increase in CO₂ levels depicted in the scatterplot. The upward trend of CO₂ levels suggests a model that accounts for an accelerating rate of change, which might make an exponential or quadratic function suitable. Specific figures mentioned, such as the pre-industrial CO₂ level of around 280 ppm and significant historical variations between 180 ppm and 300 ppm, alongside the steep, unprecedented increase over the past 50 years, indicate a considerable deviation from earlier natural cycles.
While the exact equation isn't provided without the scatterplot, understanding that CO₂ concentrations have increased by 45% since pre-industrial times and the current level being higher than in the last 800,000 years based on ice cores, we can infer that the function should encompass an exponential growth factor to accurately reflect the recent steep increase. Therefore, an exponential function of the form y(t) = a * e(bt) where a and b are constants and e is the base of the natural logarithm, could be a potential candidate for the model. It is also important to consider the context of human activities that have significantly contributed to this increase, especially since the Industrial Revolution.