(Solution) - Many fields of engineering require accurate population estimated -(2025 Original AI-Free Solution)

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Many fields of engineering require accurate population estimated. For example, transportation engineers might find it necessary to determine separately the population growth trends of a city and adjacent suburb. The population of the urban area is declining with time according to Pu(t) = Pu.max e ? kat + Pu.min
While the suburban population is growing, as in

Where Pu.max, ku, Ps.max, P0, ks, = empirically derived parameters. Determine the time and corresponding values of Pu, (t) and Ps, (t) when the suburbs are 20% larger then the city. The parameter values are Pu.max = 75,000, ku = 0.045/yr, Pu.min = 100,000 people, Ps.max = 300,000 people, p0 = 10,000 people, ks = 0.08/yr. To obtain your solutions, use
(a) Graphical
(b) False-position.and
(c) Modified secantmethods.