During a flu epidemic, the total number of students on a state university campus who had contracted influenza by the xth day was given by N(x) = 5000/1 + 49e−x    (x ≥ 0). (a) How many students had influenza initially?   (b)Derive an expression for the rate at which the disease was being spread. N'(x) =    Prove that the function N is increasing on the interval  (0, ∞). Because   N'(x)   < > = 0 ?for all x in  (0, ∞), we see that N is increasing on  (0, ∞).

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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.