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The number of geese is modeled by the function G(t) that satisfies the differential equation dG dt equals the product of G divided by 5 and the quantity 350 minus G where t is the time in years and G(0) = 100 . What is the goose population when the population is increasing most rapidly?

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sqdancefan

Answer:

  175

Step-by-step explanation:

The rate of change of the goose population is a function of the population:

  G'(x) = (x/5)(350 -x)

This function describes a downward-opening parabola with zeros at x=0 and x=350. The value of x halfway between these zeros, at x = 175, is where the maximum value of G'(x), hence the maximum rate of change, is located.

The goose population is increasing most rapidly when it is 175.

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