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IrinaK [193]
3 years ago
7

Part I On a certain university campus there is an infestation of Norway rats. It is estimated that the number of rats on campus

will follow a logistic model of the form P(t)=50001+Be−kt. A) It is estimated that there were 500 rats on campus on January 1, 2010 and 750 on April 1, 2010. Using this information, find an explicit formula for P(t) where t is years since January 1, 2010. (Assume April 1, 2010 is t=.25.
Mathematics
1 answer:
Firdavs [7]3 years ago
3 0

Answer:

Step-by-step explanation:

P(t)=50001+Be^{-kt}

If <em>t</em> is years since January 1, 2010, then on January 1, 2010, <em>t</em> = 0.

On April 1, 2010, there are 3 months from January 1, 2010. <em>t</em> = 0.25 (3 months ÷ 12 months)

At <em>t</em> = 0, <em>P</em>(<em>t</em>) = 500

P(0)=500 = 50001+Be^{-k\times0} = 50001+B

B = 500 - 50001 = -49501

At <em>t</em> = 0.25, <em>P</em>(<em>t</em>) = 750

P(0)=750 = 50001-49501e^{-k\times0.25}

49501e^{-0.25k} = 50001

e^{-0.25k} =\dfrac{50001}{49501} = 1.0101

-0.25k = \ln1.0101 = 0.01

k = -\dfrac{0.01}{0.25} = -0.04

Substituting for <em>B</em> and <em>k</em> in <em>P</em>(<em>t</em>),

P(t)=50001-49501e^{-0,04t}

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