A government agency estimates the number of young adults (ages 18 to 24) in a particular country to be 31,000 (in thousands) in 2010 and changing at the rate of −x2 + 80x − 400 thousand per year, where x is the number of years since 2010. Find a formula for the size of this population at any time x. [Hint: Keep all calculations in units of 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.