Question

the graph shows a bacteria population as a function of the number of hours since an antibiotic was introduced. what does the end behavior for x increasing without bound represent? the bacteria population will approach, but never reach, 0. the bacteria population will approach, but never reach, 1200. the bacteria population will reach 1200. the number of bacteria will approach, but never reach, 75.

Explanation:

In the context of the graph, as \(x\) (time) increases without bound, we analyze the trend of the \(y\)-axis (bacteria population). The graph shows a decay - like behavior. As \(x\) gets larger and larger, the \(y\)-values (number of bacteria) get closer and closer to \(0\) but never actually reach \(0\). This is a common end - behavior for exponential decay - related functions (where the horizontal asymptote is \(y = 0\) in this case).

Answer:

The bacteria population will approach, but never reach, \(0\).