A certain ride in an amusement park accommodated 2,394 riders by 12 P.M. and 3,986 riders by 2 P.M. At this rate, what is the total number of riders that the ride will accommodate by 9 P.M.?

To find the total number of riders that the ride will accommodate by 9 P.M., we need to find the rate at which the number of riders is increasing.

First, let's find the rate of increase in the number of riders per hour:
Number of riders by 12 P.M. = 2,394
Number of riders by 2 P.M. = 3,986
Number of hours between 12 P.M. and 2 P.M. = 2

Rate of increase per hour = (3,986 - 2,394) / 2 = 796 riders per hour

Now, we can find the total number of riders that the ride will accommodate by 9 P.M. which is 9 hours after 12 P.M.:
Number of hours between 12 P.M. and 9 P.M. = 9

Total number of riders by 9 P.M. = 2,394 + 796 * 9 = 2,394 + 7,164 = 9,558 riders

Therefore, the ride will accommodate a total of 9,558 riders by 9 P.M.