A population $$ P $$ obeys the logistic model. It satisfies the equation $$ \frac{d P}{d t}=\frac{5}{900} P(9-P) $$ for $$ P0 $$. (a) The population is increasing when 0

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A population $$ P $$ obeys the logistic model. It satisfies the equation $$ \frac{d P}{d t}=\frac{5}{900} P(9-P) $$ for $$ P>0 $$. (a) The population is increasing when 0

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To determine when the population is increasing, we need to find the values of $$ P $$ for which the derivative $$ \frac{dP}{dt} $$ is positive. Given the logistic model equation: $$ \frac{dP}{dt} = \frac{5}{900} P(9-P) $$ To find when the population is increasing, we need to find the values of $$ P $$ for which $$ \frac{dP}{dt} > 0 $$. Let's solve the inequality $$ \frac{5}{900} P(9-P) > 0 $$ to determine the intervals where the population is increasing. Solve the inequality by following steps: - step0: Solve the inequality by testing the values in the interval: $$\frac{5}{900}P\left(9-P\right)>0$$ - step1: Reduce the fraction: $$\frac{1}{180}P\left(9-P\right)>0$$ - step2: Rewrite the expression: $$\frac{1}{180}P\left(9-P\right)=0$$ - step3: Elimination the left coefficient: $$P\left(9-P\right)=0$$ - step4: Separate into possible cases: $$\begin{align}&P=0\&9-P=0\end{align}$$ - step5: Solve the equation: $$\begin{align}&P=0\&P=9\end{align}$$ - step6: Determine the test intervals: $$\begin{align}&P<0\&09\end{align}$$ - step7: Choose a value: $$\begin{align}&P_{1}=-1\&P_{2}=5\&P_{3}=10\end{align}$$ - step8: Test the chosen value: $$\begin{align}&P<0\textrm{ }\textrm{is not a solution}\&09\textrm{ }\textrm{is not a solution}\end{align}$$ - step9: The final solution is $$0The population is increasing when $$ 0 < P < 9 $$.

A population obeys the logistic model. It satisfies the
equation
for .
(a) The population is increasing when
0

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A population obeys the logistic model. It satisfies the equation for . (a) The population is increasing when 0