Function word problem

Question

Twitter monthly worldwide active users increased approximately linearly from 42 million users in 2010 to 218 million users in 2013. Let n be the number(in millions) of worldwide active users of twitter at t years since 2000. Find an equation of a linear model to describe the data.

Answer 1

 

 N(t) = M*(X-2000)+B  where M is the slope and B is the intercept

 

42 = N(2010) = M*(2010-2000)+B = 10M + B  <--- first equation

 

218 = N(2013) = M*(2013-2000)+B = 13M + B <--- second equation

 

Subtracts first equation FROM the second equation

 

176 = 3M

 

M = 176/3 =  58 and 2/3  = 58.6

 

Substitutes into the first equation:

 

42 = (176/3)(2010-2000) + B

 

42 = (176/3)(10) + B

 

42 = 1760/3 + B

 

B = 42 - 1760/3 = (126 -1760)/3 = -1634/3 = -544 and 2/3  = -544.6

 

The linear model is:

 

  N(t) = (176/3) * (t - 2000) - 1634/3

 

 

 

 

 

 

 

Answer 2

Slope = (218 - 42)/(2013 - 2010) = 176/3 

 

n = (176/3)t + 2000