The population of a city in 2005 was 18,000. By 2010 the city’s population was 45,000. Economists have determined that the population growth

Question

The population of a city in 2005 was 18,000. By 2010 the city’s population was 45,000. Economists have determined that the population growth follows an exponential model. If they are correct, what is the projected population for 2015?

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Camila 3 weeks 2021-09-26T05:40:05+00:00 1 Answer 0

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    2021-09-26T05:41:41+00:00

    Answer:

    112,547.095  million

    Step-by-step explanation:

    Data provided in the question

    Population of a city in 2005 = 18,000

    In the year 2010, the city population = 45,000

    Now to find out the projected population for 2015 we use the exponential model

     P = P(0)\times e^{rt}

    where

    P(0) = Initial population

    r = growth rate

    t = time

    e = natural log

    So,

    45,000 = 18,000 \times e^{5r}

    So

    e^{5r} = \frac{45}{18}

    5r = ln \frac{(45)}{(18)}

    r ≈ 0.1833

    Now

    P = 18,000e^{10\times0.1833}

    = 112,547.095  million

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