The population of a certain species in a limited environment with initial population 100 and carrying capacity

Question:

The population of a certain species in a limited environment with initial population 100 and carrying capacity 1000 is where t is measured in years.

(a) Graph this function and estimate how long it takes for the population to reach 900.
(b) Find the inverse of this function and explain its meaning.
(c) Use the inverse function to find the time required for the population to reach 900. Compare with the result of part (a).