The rate of increase of the number of married couples M (in thousands) in a country from 1970 to 2005 can be modeled by dM/dt = 1.218t2 − 44.72t + 709.1   where t is the time in years, with t = 0 corresponding to 1970.   The number of married couples in 2005 was 59,517 thousand.   1.  Find the model for the number of married couples (in thousands) in the country. M(t) =    2. Use the model to predict the number of married couples (in thousands) in the country in 2012. (Round your answer to the nearest integer.)  ___________(in thousands)

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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.