Precalculus

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The population of the US in 1850 was 23191876. In 1900, the population was 62947714.

a. assuming that the population grew exponentially, compute the grownth constant.

b. assuming continued growth at a constant rate, predict the population in 1950.

  • Precalculus -

    let t=0 correspond with the year 1850
    then 1900 ---> t = 50
    then 1950 ---> t = 100

    population = a( e^(kt) ) , where a is the initial population and t is the number of years since 1850
    23,191,876 = a e^0
    a = 23,191,876

    then:
    62,947,714 = 23,181,876 e^(50k)
    2.715384812 = e^(50k)
    50k = ln(2.715384812 )
    k = .019978673

    in 1950
    pop = 23,191,876 e^(100( .019978673))
    = 170,927,267

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