"After the first month" bothers me. It is not clear. All of the months, except the first, is "after the first month". If it had said "during" the first month, then I would take the number of subscribers at t= 0, 0, and at t= 1, 93.75, observe that that is a total change of 93.75 and, because that happened during one month, the "rate of change" would be 93.75 subscribers divided by 1 month= 93.75 subscribers per month.
But you my be right that "after the first month" means "during the second month". After the first month there were 93.75 subscribers and after the second month there were 120. So during that month the number of subscribers increased by 120- 93.75= 26.25. Since that was over one month, the rate of increase is 26.25/1= 26.25 subscribers per month.
Yet another interpretation of "after the first month" would be "all the months given after the first". That is, after the first month there were 93.75 subscribers. After t th month, there are 1500t/(t+3)^3. Subtract those to find the total change and divide by t- 1.
Finally, since this is a Calculus problem, the instantaneous rate of change is given by the derivative. Can you find the derivative of 1500t/(t+3)^3?