a population of bacteria is treated with an antibiotic. it is estimated that 5,000 live bacteria existed in…

Answer:

A. $f(x)=5000(0.4)^x$, with a horizontal asymptote of $y = 0$

Explanation:

Step1: Determine the decay - factor

The initial number of bacteria is 5000. After each day, 40% of the sample remains alive. The decay - factor $r$ for exponential decay is given by the proportion of the remaining amount. Here, $r = 0.4$. The general form of an exponential decay function is $y=a\cdot r^x$, where $a$ is the initial amount and $r$ is the decay factor. So the function for the number of live bacteria after $x$ days is $f(x)=5000(0.4)^x$.

Step2: Analyze the asymptote

For an exponential decay function of the form $y = a\cdot r^x$ where $0<r<1$ and $a>0$, as $x\rightarrow+\infty$, $y\rightarrow0$. So the horizontal asymptote of the function $y = 5000(0.4)^x$ is $y = 0$.