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?

Af(x) = 5000(0.4)x, with a horizontal asymptote of y = 0

Bf(x) = 5000(0.6)x, with a vertical asymptote of x = 0

Cf(x) = 5000(1.4)x, with a horizontal asymptote of y = 0

Df(x) = 5000(1.6)x, with a vertical asymptote of x = 0

"f(x) = 5000(0.4)x, with a horizontal asymptote of y = 0" is the one among the following choices given in the question that best describes the graph of the function that represents the number of live bacteria after x days of treatment. The correct option among all the options that are given in the question is the first option or option "A".

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DelcieRiveria DelcieRiveria · Answer 2 · 2019-01-23T06:20:53-05:00

Answer:

The correct option is A.

Step by step explanation:

The exponential function is defined as

\(f(x)=ab^x\)

Where, a is initial value and b is growth factor or decay factor.

The initial population of bacteria is 5000.

After each day of treatment, 40% of the sample remains alive. It means the growth factor or decay factor is

\(\frac{40}{100}=0.4\)

Therefore the required function is

\(f(x)=5000(0.4)^x\)

The horizontal asymptote is y=0 because

\(f(x)\rightarrow 0\text{ as }x\rightarrow\infty\)

Therefore option A is correct.