3) When modeling population growth of a new species (or virus), we often use the very important logistic curve P(t) =- , where A is some constant. [Note: You may have seen populations modeled...

Extracted text: 3) When modeling population growth of a new species (or virus), we often use the very important logistic curve P(t) =- , where A is some constant. [Note: You may have seen populations modeled exponentially as P(t) = Poe"t, or something similar. This model grows without bound, and so is not a very accurate in the long run. We are fancier now, and can use better models!] a. Graph P(t) on your calculator and sketch it here. Why might this model a population's growth well? b. We want to describe how fast it is growing at a given time, so we need to take the derivative [You may first want to find the derivative of e-t]. Sketch the derivative. What is lim P'(t), and what does it mean?