Question

Clara is taking a medicine for a common cold. The table below shows the amount of medicine f(t), in mg, that was present in Clara's body after time t:
t (hours) 1 2 3 4 5
f(t) (mg) 236.5 223.73 211.65 200.22 189.41


Heidi was administered 300 mg of the same medicine. The amount of medicine in her body f(t) after time t is shown by the equation below:

f(t) = 300(0.946)t

Which statement best describes the rate at which Clara's and Heidi's bodies eliminated the medicine?

Clara's body eliminated the antibiotic faster than Heidi's body.

Clara's body eliminated the antibiotic at the same rate as Heidi's body.

Clara's body eliminated the antibiotic at half of the rate at which Heidi's body eliminated the antibiotic.

Clara's body eliminated the antibiotic at one-fourth of the rate at which Heidi's body eliminated the antibiotic.

Answer 1

Answer:

Clara's body eliminated the antibiotic at the same rate as Heidi's body.

Answer 2

Answer:

Option. B is the answer.

Step-by-step explanation:

Clara is taking a medicine for a common cold. Table that shows the amount f(t) that was present in Clara's body after time t is

t (hours)      1             2           3            4             5

f(t) (mg)   236.5   223.73   211.65    200.22   189.41

Now we will find the explicit formula of geometric sequence.

f(1) = 236.5

and f(2) = 223.73

Therefore, common ratio of the sequence = $\frac{f(2)}{f(1)}=\frac{223.73}{236.5}$=0.946

So the equation will be f(t) = $236.5(0.946)^{t}$------(1)

At the same time Heidi was administered 300 mg of same medicine of the same sample.

Amount of medicine in her body f(t) after time t is shown by the equation

f(t) = $300(0.946)^{t}$----(2)

By comparing these equations 1 and 2, we find common ratio is same as (0.946), which reflects the rate of elimination of the antibiotic was same for both Clara and Heidi.

Option B is correct.