Hubbert Peak Refer to the final subsection “Logistic Model in Another Context” and Fig. 9...

Hubbert Peak Refer to the final subsection “Logistic Model in Another Context” and Fig. 9 to explore the application of the logistic equation to the oil industry, as follows.

(a) The phrase “Hubbert peak” refers to a graph not shown, the graph of y′ versus t. Sketch this missing graph from the information in the ty picture in Fig. 9. Your result should be bell-shaped, but not exactly in the same way as the Gaussian bell curve of Sec. 1.3, Example 5. Describe the differences.

(b) Show how much the pictures and arguments might differ if the inflection point occurs lower in the ty graph of Fig. 12. Explain why. Sketch a typical ty graph. Then sketch a typical ty′ graph from your ty graph, as in part (a).

Figure 12 Changes to oil reserve depletion analysis for asymmetric case.

(c) Use your results from parts (a) and (b) to discuss to what extent the logistic equation can represent oil recovery phenomena in general.