Henry is taking a medicine for a common cold. The table below shows the amount of medicine f(t), in mg, that was present in Henr
y's body after time t: t (hours) 1 2 3 4 5
f(t) (mg) 282 265.08 249.18 234.22 220.17
Greg was administered 200 mg of the same medicine. The amount of medicine in his body f(t) after time t is shown by the equation below:
f(t) = 200(0.88)t
Which statement best describes the rate at which Henry's and Greg's bodies eliminated the medicine?
Henry's body eliminated the antibiotic faster than Greg's body.
Henry's body eliminated the antibiotic at the same rate as Greg's body.
Henry's body eliminated the antibiotic at half of the rate at which Greg's body eliminated the antibiotic.
Geometric sequence general form: a * r^n For Greg, we are given the elimination of the medicine as a geometric nth term equation: 200 * (0.88)^t The amount of medicine starts at 200 mg and every hour, decreases by 12%; To compare the decrease in medicine in the body between the two, it is useful to get them in a common form; So, using the data provided for Henry, we will also attempt to find a geometric nth term equation that will work if we can: As a geometric sequence, the first term would be a and the second term would be ar where r = multiplier; If we divide the second term by the first term, we will therefore get r, which is 0.94 for Henry; We can check that the data for Henry can be represented as a geometric sequence by using the multiplier (r) to see if we can generate the third value of the data; We do this like so: 282 * (0.94)^2 = 249.18 (correct to 2 d.p) We can tell that the data for Henry is also a geometric sequence. So now, we just look at the multiplier for Henry and we find that every hour, the medicine decreases by 6%, half of the rate of decrease for Greg.
The answer is therefore that <span>Henry's body eliminated the antibiotic at half of the rate at which Greg's body eliminated the antibiotic.</span>
