Solve the problem.A model that describes the free fall of an object in a gravitational field subject to air resistance uses the equation  where v(t) is the velocity of the object, for   is the acceleration due to gravity, and  is a constant that involve the mass of the object and the air resistance. Let 

src="https://sciemce.com/media/4/ppg__tttt0613190828__f1q57g5.jpg" alt="" style="vertical-align: -4.0px;" /> For what initial values  are solutions increasing? decreasing? What is the equilibrium solution?



A. increasing for A > 24.5 and decreasing for A < 24.5; v(t) = 24.5

B. increasing for A > 24.5 and decreasing for A < 24.5; v(t) = 0

C. increasing for A < 24.5 and decreasing for A > 24.5; v(t) = 24.5

D. increasing for A < 24.5 and decreasing for A > 24.5; v(t) = 0


Answer: C

Mathematics

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