Animal populations are not capable of unrestricted growth because of limited habitat and food supplies. Under such conditions the population follows a logistic growth model: d P(t) 1 + ke-ct where c, d, and k are positive constants. For a certain fish population in a small pond d = 1000, k = 9, c = 0.2, and is measured in years. The fish were introduced into the pond at time t = 0. (a) How many fish were originally put in the pond? fish (b) Find the population after 10, 20, and 30 years. (Round your answers to the nearest whole number.) 10 years fish 20 years fish 30 years fish (c) Evaluate P(t) for large values of t. What value does the population approach ast→ o? P(t) = Does the graph shown confirm your calculations? P 1000 800 600 400 200 10 30 40 Yes No 20 O O

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Q: Biologists stocked a lake with 500 fish and estimated the carrying capacity (the maximal population…

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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.