Let's call G(t) the function that denotes the total change of customers.
And you are given the rate of change. That is G'(t) = 250 + 200t^(5/6)
In order to find the total change, you need to integrate G'(t). The you were told that G(0) = 4000 ... using this fact will give you the value for the constant C you obtain when integrating.
Then you'll just need to find G(18)