The number of new prison admissions (into state or federal facilities) between 2002 and 2011 is given by the function N(t) = −87.244444t3 − 2482.35t2 + 46009.26t + 579185    (2 ≤ t ≤ 11) where t is measured in years, with  t = 2  corresponding to 2002.† Show that the number of new prison admissions peaked in 2006 by finding the time t where N(t) has a maximum. Hint: Use the quadratic formula. (Round your answer to two decimal places.) t =     What was N(t), the highest number of new inmates, at that time? (Round your answer to the nearest whole number.)

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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.