Question

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 Henry'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 300 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) = 300(0.88)^t

Which statement best describes the rate at which Henry's and Greg's bodies eliminated the medicine?

a.) Henry's body eliminated the antibiotic faster than Greg's body.
b.) Henry's body eliminated the antibiotic at the same rate as Greg's body.
c.) Henry's body eliminated the antibiotic at half of the rate at which Greg's body eliminated the antibiotic.
d.) Henry's body eliminated the antibiotic at one-fourth of the rate at which Greg's body eliminated the antibiotic.

Answer 1

Hint 1) Try to come up with an equation for Henry's elimination rate similar to in form to Greg's elimination rate equation.

Answer 2

@retirEEd
f(t) = 300(0.94)^t

Answer 3

Graphing data points for both cases could tell y ou a lot; in fact, the graphs may solve the problem for you.

Answer 4

@mathmale is it B?

Answer 5

sorry, Nef, but unless I know how you got your result, I don't say "yes" or "no" to your choice of a, b, c, d. I've suggested a method for solving this problem; have you tried it?

Answer 6

@mathmale I made a table for Greg and an equation for Henry

Answer 7

Very good on the equation for Henry's elimination rate.

I haven't seen the a table for Greg, but I'm sure it isn't the same values as Henry's table. That's why I'm curious as to why the elimination rates are the same?

Answer 8

Thanks, @nefxrious. Are you going to post the table and equation?

Answer 9

There will likely be two different graphs that happen to intersect. At that point the elim. rates will be the same.

Answer 10

@mathmale @retirEEd
Greg:
1 2 3 5
264 231.32 204.44 15.8.31

Henry: f(t)=300(.94)^t

Answer 11

Neffy: If you haven't already, would you please graph these two sets of data on the same coordinate axes?

Answer 12

Determine the approx. coordinates of the point at which they intersect.

Answer 13

Henry: f(t)=300(0.94)^t
Greg: f(t)=300(0.88)^t

Hmmm?

Greg: (table has some questionable typos) First three values look reasonable.
1 2 3 4 5
264 231.32 204.44 ???? 15.8.31
Henry:
t (hours) 1 2 3 4 5
f(t) (mg) 282 265.08 249.18 234.22 220.17

Do Greg and Henry's elimination rates look the same?

Answer 14

@mathmale I don't have anything to graph with and i do not know what an approx is

Answer 15

@retirEEd no it doesn't it looks like Greg is going down faster

Answer 16

That is a correct observation.

Answer 17

I am sorry for having misread the question, which asks you to compare the elimination rates for two different guys. In this context, "rate" has the same meaning as "slope." You While I wouldn't say, as Neffy has, that Greg is going down faster, comparing how fast the drug is "going down" is appropriate. (The drug is 'going down;' Greg himself is not going down.)

Compare the SLOPES of the two graphs.

In the diagram below, which graph has the greater negative slope?