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

(A)Maureen's body eliminated the antibiotic faster than Kens body

Explanation:

We already have the table for Maureen, so lets figure out the table for Ken. We've been given the formula 200(0.976)^t.

we already know our starting point is 0, 200

first we substitute 1 into t, which would look like this 200(0.976)^1

So we would solve the power of 0.976 to the power of 1, which is just 0.976. so now we do 200 x 0.976 which results in 195.2. on the chart, the point would be (1, 195.2). now lets solve for the rest doing the same steps.

(2, 1905.5)

(3, 181.4)

(4, 135.5)

(5, 01.9)

Answer 2

One way to test this is by using the equation for Ken on Maureen. Let's say 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

If you compare this with Maureen's data which is 150, 90 and 54 for the first, second and third hour, respectively, you will see that Maureen's rate is much faster. However, you cannot tell by what factor because the function is exponential, not a multiple. There is no constant difference between their rates. Therefore, we only know that Maureen's rate is much faster.

The answer is Maureen's body eliminated the antibiotic faster than Ken's body.