The number of concurrent users of Skype has increased dramat

The number of concurrent users of Skype has increased dramatically since 2004. By 2013, Skype could connect concurrently 70 million users online. The exponential function P(t)=2.307(1.483)^t, where t is the number of years after 2004, models this increase in millions of users. In what year will the number of Skype users that could be online concurrently reach 54 million?

Solution

The exponential function P(t)=2.307(1.483)^t, where t is the number of years after 2004, models the increase in millions of skype users. Suppose that the number of Skype users ,that could be online concurrently reach 54 million, t years after 2004. Then 54= 2.307(1.483)^t or, (1.483)^t = 54/2.307 = 23.40702211..On taking logarith of both sides, we get t log 1.483 = log 23.40702211  = 1.369346165. Then t = 1.369346165/ log(1.483) = 1.369346165/ 0.171141151 = 8 Thus, 54 million skype users could be online concurrently in the year 2012. ( 2004+8)

Note:

The data for concurrent users of Skype in the year 2013 is incorrect. As per the formula given, it should be 80 million and not 70 million.