$($c$)$ Considering the shape of solutions for the population, give any intervals for which the following are true. If no such interval exists, enter none, and if there are multiple intervals, give them as a list. $($Thus$,$ if solutions are increasing when $P$ is between $1$ and $3,$ enter $(1,3)$ for that answer; if they are decreasing when $P$ is between $1$ and $2$ or between $3$ and $4,$ enter $(1,2),(3,4).$ Note that your answers may reflect the fact that $P$ is a population.$)$

$P$ is increasing when $P$ is in $$

$P$ is decreasing when $P$ is in $(1\mathrm{.}5,$ infinity$)$

Think about what these conditions mean for the population, and be sure that you are able to explain that.

In the long$-$run, what is the most likely outcome for the population?

$$

$P$

$($Enter infinity if the population grows without bound.$)$

Are there any inflection points in the solutions for the population? If so$,$ give them as a comma$-$separated list $($e$.$g$.,1,3)$; if not, enter none.