I am presented with the following task:
"There are 100 kids in a kindergarden. At one point, a disease breaks out. Let $y(t)$ be the number of infected children after a time $t$ days. In this scenario, a good model is that the number of infected children in proportional to $y$ and $1 - \frac{y}{100}$. Explain why the logistic equation is a good model for the disease and find an expression for $y(t)$"
I'm having a hard time seeing how I'm supposed to find a general expression for $y(t)$ with the information I'm given.