Hello!

I am struggling to understand logistic growth functions. It seems that I am given very few values to derive a solution, there are 5-10 different formulas to derive the solution out there and none of them are really connecting for me. Let me explain:

Lets take the formula: ln(y)-ln(1-y)=kt+C

I don't understand how I can solve anything when my problem only provides the following information:

Initial Population of: 250,000,000
Infected: 10,000
Rate of infection (k): .0075

Find the time that the infection reaches 50%, when will it reach 80%?

Ok, so......

Where do I input 250,000,000? What about 10,000? What is (y)? What is C?

When I tried to isolate (t) to determine the amount of time I got -.00000000000047

Another example is using the same variables, but having the equation in exponential form of:

y(t)=e^kt+C/(1+e^kt+C)

Shuffle my population values and rate of infection if you like. If I could see one example of this problem done out completely I would be set for life. That is how I learn, but I can't find an example anywhere.

I would appreciate any help you can provide, but I am very visual. I have 7 pages of someone talking about the function and it is like reading Greek.