2. The penguin population on an island is modeled by a differentiable function P of time t, where P(t) is the number of penguins and t is measured in years, for 0 < t < 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(t) = 1000e0.061 penguins per year and the death rate for the penguins on the island is modeled by D(t) = 250e0.l4 (a) What is the rate of change of the penguin population on the island at time t = 0? penguins per year. (b) To the nearest whole number, what is the penguin population on the island at time t = 40? (c) To the nearest whole number, what is the average rate of change of the penguin population on the island for 0StS 40?

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