First, note that they are asking about the average number of accumulated miles per member, so we can define #A(t) = (M(t))/(P(t)#. Careful consideration will show that this results in a factor of #10^3# (since #M(t)# is expressed in units of #10^9# while #P(t)# is expressed in units of #10^6#), which is consistent with the statement that #A(t)# will be represented in thousands.
Now, we can add a third row to the table (if desired) and calculate the value of #A(t)# for each of these values of #t# provided by using our formula for #A(t)#:
#{:(t, \|, 0 , \|, 2, \|, 4, \|, 6, \|, 8, \|, 10, \|, 12),(P(t), \|, 2, \|, 5, \|, 7, \|, 12, \|, 20, \|, 28, \|, 30), (M(t), \|, 100, \|, 250, \|, 400, \|, 700, \|, 800, \|, 1000, \|, 1700),(A(t), \|, 50, \|, 50, \|, 57.1, \|, 58.3, \|, 40, \|, 35.7, \|, 56.7):}#
This provides us with a set of points #(t, A(t))# which we can draw as a continuous piecewise function, which looks like this:
From the piecewise graph, it appears that the function #A(t)# is hitting a local minimum value around #t = 10#, which corresponds to the year 1991 (since it was stated that #t# represents the number of years since 1981.
