Step 1 :The question is asking for the limit of the function as t approaches infinity. In this case, the function is an exponential decay function, which means as t approaches infinity, the value of the function will approach 0. This is because the exponent of e is negative, which means as t increases, the value of e to that power decreases.
Step 2 :Therefore, the eventual population of the bacteria will be 0.
Step 3 :The result confirms my initial thought that as time t approaches infinity, the population of the bacteria will approach 0. This is because the function is an exponential decay function, and as t increases, the value of the function decreases.
Step 4 :Final Answer: The eventual population of the bacteria as time t approaches infinity is \(\boxed{0}\).