$4.(2$ points$)$ The graph below shows the direction field of the logistic growth differential equation for a population.

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P$^\{\backslash$prime$\}=0\mathrm{.}08$ P$\backslash$left$(1-\backslash$frac$\{$P$\}\{1000\}\backslash$right$)$

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$($a$)$ Draw the solution curve if initially there are $400$ individuals in the population. Show all the work needed to solve the problem

$($b$)$ Draw the solution curve if initially there are $800$ individuals in the population.

$($c$)$ Draw the solution curve if initially there are $1100$ individuals in the population.

$($d$)$ What is the carrying capacity of the population?