The logistic equation models the growth of a population. P(t) =  1560 1 + 25e−0.65t (a) Use the equation to find the value of k. k =  (b) Use the equation to find the carrying capacity. (c) Use the equation to find the initial population. (d) Use the equation to determine when the population will reach 50% of its carrying capacity. (Round your answer to four decimal places.)  yr (e) Use the equation to write a logistic differential equation that has the solution  P(t). dP dt =       P(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.