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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