Answer
a) The model is $y=0.24t^2 + 12.64 t -39.93.$
b) The graph is on the figure along with the points of the original data and we see that they agree well.
c) The prediction is $y=555$ so there will be $555$ million subscribers.
Work Step by Step
a) Using Wolfram Mathematica command "FindFit[Data, {a t^2 + b t + c}, {a, b, c}, t]", where
we set "Data={{5, 34}, {8, 69}, {11, 128}, {14, 182}, {17, 255}, {20, 303}}" (these are technical details on how to use the utility, if you are interested in results just use the values of the coefficients listed here) we get
$$a=0.24; b=12.64; c=-39.93$$ so we our model is
$$y=0.24t^2 + 12.64 t -39.93.$$
b) The graph and the points of the original data from the table in the problem are on the figure. We see that the model agrees well with the original data (the points are near the curve).
c) First notice that since in $1995$ $t=5$ then in $2020$ $t=30$ since it is measured in years passed. Now to predict the number of cell phone subscribers in $2020$ we just put $t=30$ in the formula from the model
$$y=0.24\times 30^2 + 12.64\times 30 -39.93 = 555$$
