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?

A) Clara's body eliminated the antibiotic faster than Heidi's body.
B) Clara's body eliminated the antibiotic at the same rate as Heidi's body.
C) Clara's body eliminated the antibiotic at half of the rate at which Heidi's body eliminated the antibiotic.
D) 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.

Step-by-step explanation:

1) Let's write the data of Clara's table just to have them ready to compare

t (hours)          1               2               3             4               5

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

Change(mg)     -          -12.77       -12.05     -11.43      -10.81

2) Now calculate the amount of medicine as per Heide's formula, 300(0.946)^t:

t (hours)             1             2                 3             4               5

f(t) (mg)           283.8    268.48         253.98     240.26      227.29

Change (mg)                 -15.12          -14.5     -13.72          -12.97

Now you can compare the data and realize that the rate of change of Heide is greater than the rate of change of Clara, meaning that Heide eliminates the medicine faster than Clara.