Question

A certain drug has a half-life of 2 hours in the bloodstream. The label says to take the drug every six hours. About how much of the drug will be in the bloodstream a month after the patient begins taking 700 mg every six hours?

a.700 mg
b.500 mg
c.800 mg

Answer 1

wow, this sounds like a geometric sum, ya? or no?

Answer 2

ya? :D lol

Answer 3

ok, so... the equation for geometric sum is:\[S_n = a_1\frac {1-r^n}{1-r}\] does this equation look like the one you are use too?

Answer 4

yes

Answer 5

so we need to find what r is , what n is, and what a_1 is
r is the ratio, can you find this?

Answer 6

but is there enough info because we only know one term

Answer 7

but i guess the rate would be 2 hours?

Answer 8

hold on... i'm going to work this all out to make sure i'm not leading you into the dark

Answer 9

okay thanks

Answer 10

I'm getting stuck :/
i'm having trouble working out the part where the medicine is taken every 6 hours...
I have an idea how to answer the question, but it uses logic more than equations...

Answer 11

yeah i can agree with that so what do u think?

Answer 12

I made a table:

n | hr | qt
0 0 700
1 2 350
2 4 175
3 6 787.5 = 87.5 + 700
4 8 393.75 = .5*787.5

do you see when we retake the medicine at hour 6, there is 87.5mg left over from the frist time we took it, but not we are adding in 700 onto it?
so the amount of medicine is growing each time we take it again.
so there is only one possible answer out of the 3 choices that it can be...
does this make sense?

Answer 13

so 800 but u saying that it doesnt add up directly

Answer 14

800 is right, becuase it can't be 700 because we see from the table that there is still medicine in their body when it's time to take the next dose. so the total amount in their body grows and grows as they take the medicine every 6 hours

Answer 15

THANKS SO MUCH!!!

Answer 16

^_^