Question

Maureen is taking an antibiotic. The table below shows the amount of antibiotic f(t), in mg, that was present in her body after time t:

t (hours) 1 2 3 4 5
f(t) (mg) 150 90 54 32.4 19.4


Ken was administered 200 mg of the same antibiotic. The amount of antibiotic f(t) in his body after time t is shown by the equation below:

f(t) = 200(0.976)t

Which statement best describes the rate at which Maureen's and Ken's bodies eliminated the antibiotic?
Maureen's body eliminated the antibiotic faster than Ken's body.

Maureen's body eliminated the antibiotic at the same rate as Ken's body.

Maureen's body eliminated the antibiotic at half of the rate at which Ken's body eliminated the antibiotic.

Maureen's body eliminated the antibiotic at one-fourth of the rate at which Ken's body eliminated the antibiotic.

Answer 1

Maureen's body eliminated the antibiotic faster than Ken's body.

Explanation:

We will use the equation for Ken on Maureen.

f(t) =
`200(0.976)^t`

So, in the first hour,

f(t) =
`200(0.976)^(1)` = 195.2 mg

In the second hour,

f(t) =
`200(0.976)^2` = 190.52 mg

In the third hour,

f(t) =
`200(0.976)^3`= 186 mg

Now, comparing these values with Maureen's, we can see that she has a faster rate of 150,90,54 in the 1st, 2nd and 3rd hours respectively as compared to Ken.

So, we can conclude that Maureen's body eliminated the antibiotic faster than Ken's body.