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(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(1.4)x, with a horizontal asymptote of y = 0
f(x) = 5000(1.6)x, with a vertical asymptote of x = 0
Answers
Given : 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.
To Find : Which best describes the graph of the function that represents the number of live bacteria after x days of treatment?
Solution:
x = 0 => f(x) = 5000 as initial is 5000
x = 1 => 5000 * (40/100) = 5000(0.4)
x = 2 =>5000(0.4) * (40/100) = 5000(0.4)²
f(x) = 5000(0.4)ˣ
Maximum value of f(x) = 5000
f(x) = 5000(0.4)ˣ is Positive
Hence no vertical asymptote
as x tends to infinity f(x) tends to 0
Hence a horizontal asymptote of y = 0
f(x) = 5000(0.4)ˣ with a horizontal asymptote of y = 0
is the correct answer
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Answer: the answer is A
Step-by-step explanation: f(x) = 5000(0.4)x, with a horizontal asymptote of y = 0