Find parameter values for a logistic differential equation that fit the crude oil production data for the U.S. (see Table 1.12).* Predicting both the growth rate and the total amount of recoverable crude oil from the data is difficult. Model the crude oil production of the U.S. assuming the total amount of recoverable crude oil in the U.S. is 200 billion barrels. (This assumption includes what has already been recovered and serves the role of the carrying capacity in the logistic model.) Repeat Part 2 replacing 200 billion barrels with 300 billion barrels. Model the world crude oil production based on estimates of total recoverable crude oil (past and future) of 2.1 trillion barrels and of 3 trillion barrels. (Both of these estimates are commonly used. They are based on differing assumptions concerning what it means for crude oil to be "recoverable.") When do the models predict that the rate of production of oil reaches its maximum? The decline in production of crude oil will certainly result in an increase in price of oil products. This price increase will provide more funds for crude oil production, perhaps slowing the rate of decline. Describe how this price increase might affect the predictions of your model for world oil production and how you might modify your model to reflect these assumptions. Your report: Present your models one at a time. Discuss how well they fit the data and how sensitive this fit is to small changes in the parameters