The population of salmon next year is given by f ( S ) = S e r ( 1 - S / P) , where S is this year's salmon population, P is the equilibrium population, and r is a constant that depends upon how fast the population grows. Find f ' ( S0 ) and solve the equation f ' ( S0 ) = 1, using a calculator to find the intersection of the graphs f ' ( S0 ) and y = 1.  Find the population for which the maximum sustainable harvest occurs if r = 0.4 and P = 750

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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.