A conservation organization releases 160 animals of an endangered species into a game preserve. The organization believes that the preserve has a carrying capacity of 1600 animals and that the growth of the herd will be modeled by the logistic curve p =  1600 1 + 9e−kt,    t ≥ 0 where p is the number of animals and t is the time (in years). The herd size is 198 after 2 years. Find k. (Round your answer to four decimal places.) k = Find the population of animals after 7 years. (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.