A journalist observes that the total number of Facebook users, between 2010 and 2015, can be modeled by the linear equation u = 213t − 1740 (10 ≤ t ≤ 15) where u is the total number of Facebook users in millions, and t is the number of years since the start of 2000.
(i) Find the number of users at the start of 2012.
(i) Find the number of users at the start of 2012.
(ii) Calculate the year in which the total number of users reaches 1000 million
(iii) Write down the gradient of the straight line represented by the equation u = 213t − 1740 (10 ≤ t ≤ 15).
What does this measure in the practical situation being modeled?
(iv) Explain why the value −1740 in the model does not imply that there were negative numbers of Facebook users at the start of 2000.
(v) Either using Graphplotter or by hand, sketch the graph of u = 213t − 1740 (10 ≤ t ≤ 15), putting u on the vertical axis, and covering the time interval 10 ≤ t ≤ 15.
(vi)How could you use your graph from part (a)(v) to estimate the year in which the total number of users passes 1000 million, and thus check your answer to part (a)(ii)
