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?

Question

Mathematics

Paisley Avery

25 September, 21:14

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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Beatrice Pierce · Answer 1

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.