At the beginning of a population study, the population of a large city was 1.65 million people. Three years later, the population was 1.74 m

Question

At the beginning of a population study, the population of a large city was 1.65 million people. Three years later, the population was 1.74 million people. Assume that population grows according to an uninhibited exponential growth model.

What would be the population of the city 5 years after the start of the population study?

A. 2.1518
B. 1.7683
C. 1.8027
D. 1.8843
F. None of the Above

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Rylee 1 month 2021-10-13T18:05:25+00:00 1 Answer 0 views 0

Answers ( )

    0
    2021-10-13T18:07:11+00:00

    Answer:

    C. 1.8027

    Step-by-step explanation:

    The exponential population growth model is given by:

    P(t) = P_{0}e^{rt}

    In which P(t) is the population after t years, P_{0} is the initial population and r is the growth rate.

    At the beginning of a population study, the population of a large city was 1.65 million people. Three years later, the population was 1.74 million people.

    This means that P_{0} = 1.65, P(3) = 1.74

    Applying this to the equation, we find r. So

    P(t) = P_{0}e^{rt}

    1.74 = 1.65e^{3r}

    e^{3r} = \frac{1.74}{1.65}

    e^{3r} = 1.0545

    Applying ln to both sides

    \ln{e^{3r}} = \ln{1.0545}

    3r = \ln{1.0545}

    r = \frac{\ln{1.0545}}{3}

    r = 0.0177

    So

    P(t) = 1.65e^{0.0177t}

    What would be the population of the city 5 years after the start of the population study?

    This is P(5).

    P(t) = 1.65e^{0.0177t}

    P(5) = 1.65e^{0.0177*5}

    P(5) = 1.8027

    So the correct answer is:

    C. 1.8027

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