A population of bacteria is treated with an antibiotic. It is estimated that 5,000 live bacteria existed in the sample before treatment. After each day of treatment, 40% 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 initial population is 5,000, so the function starts with 5000. Since 40% remains after each day, multiply the population by 0.4 for every day: f(x) = 5000(0.4)^x. This is exponential decay, and as the number of days increases, the population approaches 0 without reaching it, so the graph has a horizontal asymptote at y = 0. Choice A describes this function and asymptote.

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