Apopulation 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?

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

b. f(x) = 5000(0.6)x, with a vertical asymptote of x = 0

c. f(x) = 5000(1.4)x, with a horizontal asymptote of y = 0

d. f(x) = 5000(1.6)x, with a vertical asymptote of x = 0

The correct option is A.

Step by step explanation:

The exponential function is defined as

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

Therefore the required function is

The horizontal asymptote is y=0 because

Therefore option A is correct.

when you breathe in, or inhale, your diaphragm contracts (tightens) and moves downward. this increases the space in your chest cavity, into which your lungs expand. the intercostal muscles between your ribs also enlarge the chest cavity. they contract to pull your rib cage both upward and outward when you inhale.