Notice also that the sequence t is really just a special case of f. That is f(n) = t(n) for all natural numbers n.
Hence it suffices to find all x, for which f(x) = 200, and check if any of these x are integers. The function f is strictly increasing: This means that when x gets larger, the value f(x) also gets larger. This means in turn that there can be at most one value of x, for which f(x) = 200. What is this value? You need to solve the equation
5*2^x = 200
for x. First divide both sides by 5 to get
2^x = 40.
Do you know logarithms? If you do, use them to find x. You will get x = log(40)/log(2) (be sure to understand this (but only if you know logarithms)). This value of x is not an integer.