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

Explanation:

Step1: Identify decay factor

Since 40% of bacteria remain alive each day, the decay factor is $0.4$.

Step2: Define exponential decay function

Initial population is 5000, so the function is $f(x) = 5000(0.4)^x$.

Step3: Find horizontal asymptote

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

Answer:

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