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algebra 2/trig

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The population of a city is p=2500 e^(kt) where t = 0 represents the year 2000. in 1945 the population was 1350. Find the value of k and use this result to predict the population in the year 2010.

  • algebra 2/trig -

    if the year 2000 matches t = 0, then
    the year 1945 matches t = -55

    so we have 1350 = 2500e^(-55k)

    .54 = e^(-55k)
    using natural logs,

    -55k = ln(.54)
    k = .011203384

    so the equation is p = 2500e^(.011203384t)

    in 2010 , t = 10
    so
    p = 2500E(.011203384*10)
    = 2796

  • algebra 2/trig -

    You are a god.

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