Clara is taking a medicine for a common cold. Her body metabolizes the medicine over a certain time interval. 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.

(t) = 300(0.946)t

Question

Clara is taking a medicine for a common cold. Her body metabolizes the medicine over a certain time interval. 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.

(t) = 300(0.946)t

anonymous · Answer

Which statement best describes the rate at which Clara 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.

whpalmer4 · Answer

for each value in the table, calculate the corresponding value from the function.  Now divide one by the other.  repeat for the other values in the table.  Is that quotient always the same?  What does that imply about rate at which the medicine was eliminated?

anonymous · Answer

Ohhh yes they are the same, it is .946 meaning just like the rate of change im Heidi's body meaning that they are eliminating the antibiotic at the same rate, therefore being answer b. Thank you! @whpalmer4