Question 1089550
i believe the formula is:


f(T) = 53000 / (1 + 1059 * e ^ (-1.5 * T))


the parentheses are necessary to ensure a correct interpretation of the problem.


if i understood the formula correctly, then e^(-1.5 * T) is the same as 1 / e^(1.5 * T) and the formula would look like this:


f(T) = 53000 / (1 + 1059 / (e ^ (1.5 * T))


as T approaches infinity, then 1059 / (e ^ (1.5 * T)) approaches 0 and the formula becomes:


f(T) = 53000 / 1 which is equal to 53000.


therefore, the limiting size of the population that becomes ill is 53000.


i checked this out graphically and determined that it is correct.


T represents the number of weeks since the onset.


in the graph, y represents f(T) and x represents T.


the graph looks like this:


<img src = "http://theo.x10hosting.com/2017/080301.jpg" alt="$$$" </>