Question

An antibiotic is added to a bacteria culture. The function, n(t), represents the count of bacteria alive with respect to time in seconds in an exponential manner.

n(t) = 8,000(0.79)t


What is the asymptote and y-intercept of the function that represents the count of bacteria alive?

A.
asymptote: y = 1
y-intercept: (0 , 6,000)
B.
asymptote: y = 0
y-intercept: (0 , 5,000)
C.
asymptote: y = 1
y-intercept: (0 , 8,000)
D.
asymptote: y = 0
y-intercept: (0 , 8,000)

Answer 1

Answer: the answer is a i checked and got it right

A.

asymptote: y = 0

y-intercept: (0 , 8,000)

B.

asymptote: y = 1

y-intercept: (0 , 8,000)

C.

asymptote: y = 0

y-intercept: (0 , 5,000)

D.

asymptote: y = 1

y-intercept: (0 , 6,000)

Answer 2

D.

• Asymptote: y = 0
• y-intercept: (0 , 8000)

Explanation:

Exponential functions of the form
`y=a(b^x)+c` always have an horizontal asymptote at y=c

The y-intercept is the value of the function when x=0

In the given function

`n(t) = 8,000(0.79)^t`

The asymptote, y=0

If t=0

`n(0) = 8,000(0.79)^0=8000`

Therefore:

Aymptote: y=0

y-intercept: (0,8000)

The correct option is D.