quadratic population?

1.the populationof Parabolla land is P(t)=200-5t+0.5t^2

p is measured in thousands and t is in years after 1970

what is the initial population?

2.what does the model predict, to the nearest person, that the population parabola land will be in 2010?

Update:

3. in what month and year will the population reach 400 thousand pl?

4.what is the minimum population reached by the parabola land?

1 Answer

Relevance
  • 9 years ago
    Favorite Answer

    1.) P(t) = 0.5t² - 5t + 200

    Initial Population = 200,000

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    2.) t = 2010 - 1970

    t = 40

    P(40) = 0.5 (40)² - 5 (40) + 200

    P(40) = 0.5 (1600) - 200 + 200

    P(40) = 800

    Population in 2010 = 800,000

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    3.) P(t) = 400,000

    0.5t² - 5t + 200 = 400

    0.5t² - 5t = 400 - 200

    0.5(t² - 10t) = 200

    t² - 10t = 200 / 0.5

    t² - 10t = 400

    t² - 10t + 25 = 400 + 25

    (t - 5)² = 425

    t - 5 = √425

    t - 5 = ± 20.6155

    t = 5 ± 20.6155

    If t = 5 + 20.6155,

    t = 25.6155

    If t = 5 - 20.6155,

    t = - 15.6155

    Feassible Domain: t > 0

    Since t = - 15.6155 is not in the feasible domain,

    t = 25.6155

    Year = 1970 + 25.6155

    Year = 1995.6155

    Month = 12 (0.6155)

    Month = 7

    Population reached 400,000 in July, 1995

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    Miniumum Population: P'(t) = 0:

    P'(t) = t - 5

    t - 5 = 0

    t = 5

    Minimum population was reached in 1975.

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    Source(s): 4/5/12
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