This tries to get you into some of the backgrounds of the current situation. The math behind this is a little more complicated than it appears here and some of the results are not realistic at all. It ignores the influence of recovery from an infection which is a huge factor right now. But it should be instructive to get you started! Assume a finite set I0 with a0 = | I0 |. This set represents a group of people infected by a new virus. Each infected person comes in contact with an average number E of uninfected people. Here assume E = 17. A certain percentage p of these contacts become infected. Here assume p = 19%. [0.5 points] How many people will become infected (on the average) by one infected person? (Don't round the result!) [0.5 points] What is a1? (The number of people infected one day later, round here to the next integer - - we don't infect 0.23 people!) [1 point] Give a closed formula for an (Don't round here - rounding issues will become less noticeable with large numbers) [1 point] Classify the sequence {an} as arithmetic, geometric, both, neither. [0.5 point] Compute a30 (the number of people infected after around one month). You have just discovered the basic mechanism of "exponential growth". You have also discovered (just by looking at the value of a30) that that's very definitely not going to happen [1 point] Give at least two reasons why this growth is not realistic. [0.5 point] Compute a30 assuming E = 6 (a0 and p unchanged) [It's still terrible, don't get me wrong...]