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

P_u(t) = P_u.maxe ^{? kat} + P_u.min

While the suburban population is growing, as in

Where P_u.max, k_u, P_s.max, P₀, k_s, = empirically derived parameters. Determine the time and corresponding values of P_u, (t) and P_s, (t) when the suburbs are 20% larger then the city. The parameter values are Pu_.max = 75,000, k_u = 0.045/yr, P_u._min = 100,000 people, P_s.max = 300,000 people, p₀ = 10,000 people, k_s = 0.08/yr. To obtain your solutions, use

(a) Graphical

(b) False-position.and

(c) Modified secant methods.

Pmas Ps.mas P.(i) = 1+[P,max /Po - lJe-k