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

Step-by-step explanation:

The function is modeled after

where a is the initial amount and b is the growth/decay factor. If we start with 5000 bacteria, then a = 5000. The decay factor is determined by the rate at which the bacteria decrease. We know that rate at which the bacteria decrease is 60% because 40% are left alive; therefore, b = .4:

with a horizontal asymptote of y = 0, the first choice.

step-by-step explanation:

f(gx)=f(1/x+2)

=(1/x+2)+2

=(1+2x)/2+2

=(1+2x+4)/2

= (2x+5)/2

x^3-4x^2+3x-2/x^2+1

step-by-step explanation:

factor the numerator and denominator and cancel the common factors