Question

The table below shows the populations of four towns in the 2000 and 2010 censuses. Aztec's and Bloomfield's populations are changing exponentially while Cortez's and Durango's populations are changing linearly. Town 2000 Pop. 2010 Pop. Aztec 9,000 9,900 Bloomfield 12,000 10,800 Cortez 15,000 15,900 Durango 18,000 16,800 In 2020, Aztec's population will be how much greater than Bloomfield's population?

Answer 1

Formula : Exponential Growth on Decay P(t) = Poe kt where Plt) Population at time t Initial population Rate of growth (when kyo) Rate of decay (when ko) Po K time. In 2000, 2010 Aztec population was 9000 population , 9900 So population increases exponentially P (t) Poe 10K 9900 9000 e [it= 10 years 9.9 90 kt 10K =le Again in 2020, 10K P (t) = 9900 xe [ 2010—2026 it = 10 year 9900 x 10 = 10,890

Bloomfield population was 12000 In 2000, 2010, 10,800 So population decays exponentially kt P (t) = Poe *P(10) = Po e lol lok - 10,800 12000 e 10K =) e 10800 12 too 9 10 Again in 2020 i en 10 years later P (t) = Poekt = P(10) = Po e lot 11 10, 800 x elok 10, 800 x 9 10 9720 In 2020, Bloomfield's population will be 9720. So In 2020 Az tec's population 2 will be (10,890 - 9,720) 1170 greater than Bloomfield's population.