Math  /  Calculus

Question(1 point) A population PP obeys the logistic model. It satisfies the equation dPdt=31300P(13P)\frac{d P}{d t}=\frac{3}{1300} P(13-P) for P>0P>0. (a) The population is increasing when \square <P<<P< \square (b) The population is decreasing when P>P> \square

Studdy Solution
To determine where the population is decreasing, analyze the sign of dPdt\frac{dP}{dt} outside the interval 0<P<130 < P < 13.
Consider the interval P>13P > 13.
In this interval, P>13P > 13 implies 13P<013 - P < 0, so dPdt=31300P(13P)<0\frac{dP}{dt} = \frac{3}{1300} P(13-P) < 0.
Therefore, the population is decreasing when P>13P > 13.
The answers are: (a) The population is increasing when 0<P<130 < P < 13. (b) The population is decreasing when P>13P > 13.

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