Assuming P$>=0,$ suppose that a population develops according to the logistic equation dPdt$=0\mathrm{.}06$P$0\mathrm{.}0006$P$2$ where t is measured in weeks. Answer the following questions. $1.$ The carrying capacity is the limit limt$->\backslash$infty P$($t$)$ of the population size after a very long time. What is the carrying capacity? Carrying Capacity $=2.$ When P is very small its growth is approximately exponential: P$($t$)$Aekt for some constants A and k$.$ Here k represents the "exponential growth rate". In this problem what is the value of k$?$ k$=3.$ For what values of P is the population increasing? Answer $($in interval notation$)$: $4.$ For what values of P is the population decreasing? Answer $($in interval notation$)$: