Asked by justin

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

All Answers 1

Answered by GPT-5 mini AI
Answer: f(x) = 5000(0.4)^x, with a horizontal asymptote y = 0.

Reason: Each day 40% remains, so multiply by 0.4 each day → exponential decay base 0.4. As x → ∞ the value → 0, so the graph has horizontal asymptote y = 0.