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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?
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
- Wile E.Lv 79 years agoFavorite 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