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
Rate of infection (k): .0075
Find the time that the infection reaches 50%, when will it reach 80%?
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:
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.