Consider the exponential function defined by the equation $$f(t) = a imes b^{ct}$$, where $$a$$, $$b$$, and $$c$$ are constants. Suppose that we have two time points: $$t_1 = 0$$ and $$t_2 = 3$$. At these times, the function outputs the following values:

$$f(0) = 50$$

$$f(3) = 200$$

Using the information given, determine the value of the constant $$c$$ if it is known that $$b = 2$$.