Since, we are given table for x and y values
and table for average rate of changes
we can see the pattern of average rate of change
average rate of change for 5 to 6 is three times average rate of change for 4 to 5
but we have to find
average rate of change for 7 to 8
so, using same pattern
average rate of change for 6 to 7 is three times average rate of change for 5 to 6
average rate of change for 7 to 8 is 3*3( average rate of change for 5 to 6)
so, we can plug value
average rate of change for 7 to 8 is 3*3*486
average rate of change for 7 to 8 is 4374
so, option-D...........Answer