ollowing table shows natural gas production N in trillions of cubic feet in the United States t years after 1940. t = years since 1940 N = cubic ft. in trillions 0 3.75 10 8.48 20 15.09 30 23.79 40 21.87 50 21.52 60 24.15 (a) Make a logistic model for N as a function of t. N(t) = 12.54 1 + 5.94e−0.35t N(t) = 29.53 1 + 7.58e−0.88t N(t) = 23.31 1 + 6.99e−0.14t N(t) = 34.86 1 + 8.54e−0.91t N(t) = 35.67 1 + 3.41e−1.25t (b) Graph the data and the logistic model. WebAssign Plot WebAssign Plot WebAssign Plot WebAssign Plot (c) Which year's production was farthest from the prediction of the logistic model?

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Differential Equations

Have you ever observed the movement of the satellites and rockets or how the planets go around the sun in their orbits? How will you determine their motion? Definitely they follow some scientific laws and these kinds of problems are framed as differential equations.