US Oil Production Let P(t) be the total amount of oil (in billions of barrels) produced in the US since 1859, the year that oil production began. Assume that P(t) grows according to the logistic model = kP (1 3). dt L 3. What is the meaning of L in this context? 4. The data below are based on estimates for both P and E for the years 1931-1950. A cit best t line is shown with its equation. Use it to estimate k and L. (Hint: %% = k (1 g). The expression on the right of that equation is the best t line...) 0.0? 0.055 . (HPJ dedI =U.IJ 6434311003? 0 P I: on !=' I: a! a! (up) amt (relatlve growth late) 0.05 - El EH15 I [I I 5 ZEI 25 3B 35 40 F' (billions oiharlals) 5. If we let 1950 be time t = 0, then P(0) = 40.9 billion barrels. Find a formula for P(t). You may use the solution to the logistic equation given at the top of the previous page. 6. According to this model, what year will oil production peak in the US and what will be the peak oil production amount? (Hint: if total oil produced is P(t), what is oil production per year? Now use the info at the top of the previous page.)