The number of U.S. users (in millions) on Facebook, a computer social network, in 2009 is given in the table below.

a. Plot the data. What type of function appears to best match this data?

b. Use the regression feature on your graphing calculator to find a quartic equation that models the number of years, t, since birth and the number of Facebook users, N(t). Use the midpoint value to estimate the point in each interval for the age of the Facebook user. Graph the function with the plot of the data. Does the function resemble the data?

c. By finding an appropriate constant k, find a function S(t) = KN(t) that is a probability density function describing the probability of the age of a Facebook user.

d. For a randomly chosen person who uses Facebook, find the probabilities that the person was at least 35 but less than 45 years old, at least 18 but less than 35 years old, and at least 45 years old. Compare these with the actual probabilities.

Transcribed Image Text:

Age Interval (years) 13-17 18-25 26-34 35-44 45-54 55-65 Total Midpoint of Interval (year) 15 21.5 30 39.5 49.5 60 Number of Users in Each Interval (millions) 6.049 19.461 13.423 9.701 4.582 2.849 56.065