Question

On March 31, 2009, Facebook had 197 million monthly users worldwide and on March 31, 2012 had 901 million monthly users. If the relationship between the time and number of users is linear, predict the number of users on March 31, 2014.

Answer 1

Answer: 1370.33 millions

Explanation:

Let x be the number of years and y be the the number of users (in millions) of after x years.

Given: On March 31, 2009,company has 197 million monthly users . Let x=0 at year 2009.

So when x=0, y=197

On March 31, 2012 had 901 million monthly users.

So when x=3, y=901

Since, the relationship between the time and number of users is linear then the rate of change must be constant through out the years.

The rate of change=
`m=(y_2-y_1)/(x_2-x_1)=(901-197)/(3-0)=(704)/(3)`

The number of users after x years is given by :-

`y=197+((704)/(3))x`

The number of users on March 31, 2014 (x=5) is given by

`y=197+((704)/(3))(5)\\\Rightarrow\ y=1370.33`

Hence, the number of users on March 31, 2014 = 1370.33 millions.

Answer 2

In this item, we mark March 31, 2009 as our base or time zero. The equation that can be generated from the given first set of data for 2009 and 2012 is,
P = 197 + (901 - 197)x/3
Where P is the population and x is the number of years. Determining the value of x, we get an answer of x = 234.67
For n = 5.
P = 197 + 234.67(5) = 1370.3333
Thus, the number of users on March 31, 2004 is approximately 1370.33 million monthly users.