A recent trend in advertising is viral marketing. The goal is to convince viewers to share and amusing advertisement by email or social networking. Imagine that the video is sent to 100 people on day 1. Each person agrees to send it to 5 people the next day then those people agree to send it to 5 more people the next day. The number of viewers v(n) is an exponential function of the number of n days since the video was shown

On day zero, 100 people viewed the video. On day one, each of the 100 persons share the video with 5 persons. So 500 people watched the video. On day two each of the 500 person agrees to share the video with 5 persons so we have that 2,500 watched the video on day 2. I'll attempt to create the exponential function by trial and error. It looks like 100 and 5 are common factors in the number of viewers. So v(n) where n is the number of day and v is an exponential function of n. If V(n) = 100 * 5^(n) . Let's substite and see. So on day zero, we have 100 * 5^(0) = 100 * 1 = 100 and on day two, we have 100 * 5^(1) = 500; and on day 2 we have 100 * 5^(2) = 100 * 25 = 2, 500. Hence v(n) = 100 * 5^(n) I