The number of U.S. users (in millions) on Facebook, a computer social network, in 2018 is given in the table below.

(a) Plot the data using the midpoint and number of users in each interval. What type of function appears to best match these 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 probable 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 50 years old, at least 18 but less than 30 years old, and at least 40 years old.

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Age Interval (years) 13-17 18-24 25-34 35-44 45-54 55-64 Total Midpoint of Interval (year) 15 21 29.5 39.5 49.5 59.5 Number of Users in Each Interval (millions) 6.8 39.4 58.3 42.4 35.4 26.5 208.8