Exponential / Logistic. Growth of Facebook.com The black points plotted below represent the number of active Facebook users u, in millions, t months after.

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Exponential / Logistic

Growth of Facebook.com The black points plotted below represent the number of active Facebook users u, in millions, t months after December For example, in December 2005, there were about 5.5 million active users, so the point (12, 5.5) is shown. The data ends in July The blue graph shows an exponential model for Facebook's growth. The green graph shows a logistic model.

Exponential Growth & Decay General Form of an Exponential Function: y = a(b) x, where a = initial value and b = growth f actor Exponential growth: 1 + rate Exponential decay: 1 - rate

A social networking website is started by a group of 10 friends. They advertise their site before they launch, and membership grows fast: the membership doubles every day. At this rate, what will the membership be in a week? When will the membership reach 100,000?

Solution 10(2 x ) = 100,000 2 x = 10,000 log2 x = log10,000 xlog2 = 4 x = 4/log2 = 13.3