Question

Required information Many fields of engineering require accurate population estimates. 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,maxe−kut+Pu,min while the suburban population is growing, as in Ps(t)=Ps,max1+(Ps,max/P0−1)e−kst where Pu,max, ku, Ps,max, P0, and ks are empirically derived parameters. The parameter values are Pu,max = 80,000, ku = 0.05/yr, Pu,min = 110,000 people, Ps,max = 320,000 people, P0 = 10,000 people, and ks = 0.09/yr. Use the false-position method to determine the time and corresponding values of Pu(t) and Ps(t) when the suburbs are 20% larger than the city. (Round the values of time to four decimal places, and round the value of Pu(t) and Ps(t) to the nearest integers.)

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