The number of U.S. citizens aged 65 years and older from 1900 through 2050 is estimated to be growing at the rate of ?(?) = 0.063? 2 − 0.48? + 3.87 (0 ≤ ? ≤ 15) million people/decade, where t is measured in decades, with ? = 0 corresponding to 1900. Show that the average rate of growth of U.S. citizens aged 65 years and older between 2000 and 2050 will be approximately twice the average rate between 1950 and 2000.

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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.