A population of bacteria is treated with an antibiotic. It is estimated that 5 comma 000 live bacteria existed in the sample before treatment. After each day of treatment, 40 percent of the sample remains alive. Which best describes the graph of the function that represents the number of live bacteria after x days of treatment?

The sample starts with 5,000 live bacteria, so the initial value is 5,000. If 40% remain alive each day, the population is multiplied by 0.4 each day, giving f(x) = 5000(0.4)^x. This is exponential decay, and its values approach 0 as x increases, so the graph has a horizontal asymptote at y = 0. Therefore, the correct choice is B.

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