Calculator Help for Model Solutions

Let’s continue with the model from the previous notes. We found that the CO₂ concentration model is:

CO₂(t) = 1.38t + 319.02

(This equation should be in Y1 in terms of X to create the table of values to help with the needed calculations on most models.)

Suppose we want the concentration in 2010, according to our model. 2010 – 1965 = 45 is the t-value we need because the baseline year is 1965. On the calculator, do the following:

1. 2^ND TABLE (over GRAPH). Here you will see a table labeled with X (t-values) and Y1 (predicted values from the model).
2. To get at 45 quickly, 2^ND TBLSET (over WINDOW). At Tblstart, type in 45, then 2^ND TABLE. Recall that the settings on 2^ND TBLSET should read AUTO in both locations. The calculator goes immediately to 45 in the table and tells you the concentration for 2010 is predicted for 381.12 ppm.

Suppose we want to know what year the model predicts that the concentration will reach 425 ppm. On the calculator, do the following:

1. We already know from the earlier calculation that t = 45 gives us a concentration of 381.12 ppm. So, estimate a t-value for 425 ppm—say 60.
2. 2^ND TBLSET (over WINDOW). At Tblstart, type in 60, then 2^ND TABLE. The calculator tells us that the concentration at t = 60 is 401.82 ppm. So, use the blue down button to scroll down to 425 ppm. Notice that 425 ppm does not appear in the table.
3. The nearest value without going over is t = 76. Use this value. Now, to get the year this happens, use the baseline year: 1965 + 76 = 2041 is the year the model predicts the concentration to be 425 ppm.