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.
I can help with this one
but can not really tell what you want because you have not bracketed it to be clear.
In mathematics, you don't understand things. You just get used to them.
I have the result, but I do not yet know how to get it.
All physicists, and a good many quite respectable mathematicians are contemptuous about proof.