Answer
(a)
$t=200$
$P(200)\approx11.7911$ Billions
$t=300$
$P(200)\approx11.9713$ Billions
(b) See the graph below.
(c) According to this model, the world population seems to approach $12$ Billions.
Work Step by Step
According to the information provided we have the following function:
$P(t)=\frac{73.2}{6.1 + 5.9e^{-0.02t}}$
Where $t$ stands for years passed after $2000$ year.
(a) In the year $2200$ we have $t=200$
$P(200)=\frac{73.2}{6.1 + 5.9e^{-0.02\times200}}=\frac{73.2}{6.1 + 5.9e^{-4}}\approx11.7911$ Billions
In the year $2300$ we have $t=300$
$P(200)=\frac{73.2}{6.1 + 5.9e^{-0.02\times300}}=\frac{73.2}{6.1 + 5.9e^{-6}}\approx11.9713$ Billions
(b) See the graph above. Note, $t$ stands for years passed after the year $2000$
(c) According to this model, the world population seems to approach $12$ Billions. Which, according to the information, is the amount the planet can support.