The population of a southern city the exponential law If the

The population of a southern city the exponential law. If the population doubled in size over 11 months and the current population is 10,000, what will the population be 5 years from now? What will the population be 5 years from now? The population will be approximately people.

Solution

Let the exponential law which the population of the Souther city follows be A = A₀ b^kt where A₀ is the initial population, A is the population after t months, b is an arbitrary real number, and k is the constant of growth. Here, A₀ = 10000, A = 20000 when t = 11 so that 20000= 10000 b^11k or, b^11k = 20000/10000 = 2. Further, the population after 5 years will be A = 10000b^5*12k = 10000b^60k = 10000(b^11k)^60/11 = 10000(2)^60/11 = 10000*43.85123149= 438,512.31 or, 438512 ( on rounding off to the nearest whole number). Thus, the population of the Souther city will be approximately 438512 after 5 years.