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:

D.

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

Step-by-step 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.