#### Answer

(a) On the graph, we can see that the population reaches 900 after approximately 4.5 years.
(b) This function tells us how much time is required (in years) for a population to reach a level of $P$.
(c) It takes 4.4 years for the population to reach 900.

#### Work Step by Step

(a) On the graph, we can see that the population reaches 900 after approximately 4.5 years.
(b) We can find the inverse:
$P = \frac{100,000}{100+900e^{-t}}$
$100+900e^{-t} = \frac{100,000}{P}$
$900e^{-t} = \frac{100,000}{P}-100$
$e^{-t} = \frac{1}{900}\cdot(\frac{100,000}{P}-100)$
$-t = ln[\frac{1}{900}\cdot(\frac{100,000}{P}-100)]$
$t = -ln[\frac{1}{900}\cdot(\frac{100,000}{P}-100)]$
This function tells us how much time is required (in years) for a population to reach a level of $P$.
(c) We can find the time required for the population to reach 900:
$t = -ln[\frac{1}{900}\cdot(\frac{100,000}{P}-100)]$
$t = -ln[\frac{1}{900}\cdot(\frac{100,000}{900}-100)]$
$t = -ln(0.012345679)$
$t = 4.4$
It takes 4.4 years for the population to reach 900.