This is a three-part problem. Suppose the population P of rainbow trout in a fish hatchery is modeled by the differential equation dP/dt = P(3-P). In this equation, P is measured in thousands of trout and t is measured in years. Suppose P(0) = 1. I) Find a formula for the population at any time. II) What is the size of the trout population after a very long time? III) At what time is the trout population increasing most rapidly?

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A: Use the logistic differential equation to find out the answers shown below.

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A: This question is related to differrential equations, We will solve it using given information.

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Q: The tank in the figure contains 4000 L of water in which initially 50 kg of salt is dissolved. Brine…

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A: The complete solutions are given below

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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.