Question

The exponential model A = 999.8 0.002t describes the population, A, of a country’ in millions, t years after 2003. Use
the model to determine when the population of the country will be 1051 million?

Answers

  1. The population of the country will be 1051 million in 2014

    How to model the population of the country?

    The exponential model that describes the population of a country’ in millions, t years after 2003 is given as:
    A = 999.8 e0.002t
    Rewrite the function properly as:
    A = 999.8 * e^(0.002t)
    When the population of the country is 1051 million, it means that:
    A = 1051
    Substitute the known values in the above equation
    So, we have:
    1051 =  999.8 * e^(0.002t)
    Divide both sides by 999.8
    1.0512 = e^(0.002t)
    Take the natural logarithm of both sides of the equation
    ln(1.0512) = ln(e^(0.002t)
    Rewrite the equation as:
    ln(e^(0.002t) = log(1.0512)
    This gives
    0.002t = log(1.0512)
    Evaluate the logarithmic expression
    0.002t = 0.0216
    Divide both sides of the equation by 0.002
    t = 0.0216/0.002
    Evaluate the quotient
    t = 10.8
    Approximate 10.8 as 11
    t = 11
    11 years from 2003 is 2014
    Hence, the population of the country will be 1051 million in 2014
    Read more about exponential functions at:
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