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21 August, 01:02

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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  1. 21 August, 01:19
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    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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