Chapter 3.4, Problem 87E

Since the 1950s, the carbon dioxide concentration in the air has been recorded at the Mauna Loa Observatory in Hawaii.¹³ A graph of this data is called the Keeling Curve, after Charles Keeling, who started recording the data. With t in years since 1950, fitting functions to the data gives three models for the carbon dioxide concentration in parts per million (ppm):

$\begin{array}{l}f(t)=303+1.3t\\ g(t)=304e^{0.0038t}\\ h(t)=0.0135t^2+0.5133t+310.5\end{array}$

1. (a) What family of function is used in each model?
2. (b) Find the rate of change of carbon dioxide in 2010 in each of the three models. Give units.
3. (c) Arrange the three models in increasing order of the rates of change they give for 2010. (Which model predicts the largest rate of change in 2010? Which predicts the smallest?)
4. (d) Consider the same three models for all positive time t. Will the ordering in part (c) remain the same for all t? If not, how will it change?