Question

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?
$f(x)=5000(1.6)^x$ with a vertical asymptote of $x=0$
$f(x)=5000(1.4)^x$ with a horizontal asymptote of $y=0$
$f(x)=5000(0.6)^x$ with a vertical asymptote of $x=0$
$f(x)=5000(0.4)^x$ with a horizontal asymptote of $y=0$

Explanation:

Step1: Identify decay factor

Since 40% of the sample remains alive each day, the decay factor is $0.4$. The initial population is 5000, so the function is $f(x)=5000(0.4)^x$.

Step2: Determine asymptote

For exponential decay functions of the form $f(x)=ab^x$ where $0

Answer:

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