The penguin population on an island is modeled by a differentiable function Pof time t, where P(t) is the number of penguins and tis measured in years for 0 sts 40. There are 100,000 penguins on the island at time t = 0. The birth rate for the penguins on the island is modeled by B(1) = 1000e0.06t penguins per year and the death rate for the penguins on the island is modeled by D1)=250e0. 1" penguins per year. To the nearest whole number, what is the penguin population on the island at time t= 40?

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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.