The population x of a certain city satisfies the logistic law dx/dt = 1/100 x − 1/(10)^8 x^2 where time t is measured in years. Given that the population of this city is 100,000 in 1980, determine the population as a function of time for t > 1980. In particular, answer the following questions: a)What will be the population in 2000? b)In what year does the 1980 population double?

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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.