A population P\displaystyle {P} obeys the logistic model. It satisfies the equation
dPdt=9900P(9−P)\displaystyle {\frac{{{d}{P}}}{{{\left.{d}{t}\right.}}}}={\frac{{{9}}}{{{900}}}}{P}{\left({9}-{P}\right)} for P>0.\displaystyle {P}>{0}.

(a) The population is increasing when   <P<\displaystyle <{P}<  

(b) The population is decreasing when P>\displaystyle {P}>  

(c) Assume that P(0)=4.\displaystyle {P}{\left({0}\right)}={4}. Find P(81).\displaystyle {P}{\left({81}\right)}.
P(81)=\displaystyle {P}{\left({81}\right)}=  

License