Math Help - Logistic function

1. Logistic function

We all know that with an exponential function, we can use it to approximate population. With a logistic function, it simply adds on a carrying capacity to the population (Where the population cannot grow anymore at a certain level):
L
---------
1 + Ce^(-kt)

where, L is the carrying capacity
t - time in years
and k/C are constants

I have a question asking me to compare the predicted population using the logistic function and compare it to the governments population prediction method.

All I could think of is to graph it to show the scatterplot discrepancies and to use percentage error to show how accurate/inaccurate the logistic function would fit into the real population the government has predicted.
(Of course, I have assumptions to be made on the function)

Now, I think the question given is really a high-order maths question.. so I thought if algebra can come into this?

Anyone have any idea to make the answer to this question a higher-order maths level? If its using algebra, please teach me. Cheers!

Any help would be very much appreciated~

2. What is "the government's population prediction method"?

3. Good question!
They use extrapolation involving geometric rates of increase or.. usually they use simple ratios.. / patterns assuming that there're no wars

or.. 2nd degree / 3rd degree parabolas.. !