Question

I give medals!!!

Patrick was sick and had to take 50 mg of antibiotics each day for 2 weeks. Each day he takes his medicine the amount in his body doubles. How much medicine will be in his body at the end of the 2 weeks?
A. 700 mg
B. 1400 mg
C. 409,600 mg
D. 819,200 mg

Answer 1

700, but the amount doubles each day, making this a geometric sequence. Day two being 100mg, day 3 being 200mg, day 4 being 400mg. etc.

Answer 2

Right, then is that the answer you got?

Answer 3

some what. I dont know how id show my work using the formula though

Answer 4

no i dont know how to do it, so i didnt get anything different

Answer 5

What formula did they give you?

Answer 6

\[a _{n} = a _{1} \times r ^{(n-1)}\]

Answer 7

I honestly have no clue how that formula would be used for this...

Answer 8

the answer is C
Working:
since the amount doubles each day he takes the dose,
on the first day, his body would have 50mg
on the second, 2x50
on the third, 2x2x50
on the fourth,2x2x2x50
this would go on till the fourteenth day
this forms a geometric series which i figure you know about
the GS is 50,100,200,400,...,gn
the nth term of a geometric series is given by an=a1r^(n-1)
in this case a1=50 (first term in the series)
and n=14 (number of terms=number of days he'll have to take the dose)
and r is the common ratio, which you can get by dividing any of the terms by the one RIGHT BEFORE it
thus gn=50*2^(14-1)=409600
therefore the amount the antibiotic in his body by the end of the 2 weeks would be
409,600 mg

Answer 9

50*2^(14-1)=409600

I had just put that into the calculator and found that answer. I wasn't sure if was correct. Makes sense now, thanks @fatma01 (I wanted to say batman) lol
Disregard my posts @Tessa_Mae I am sorry.

Answer 10

haha you're welcome

Answer 11

thankyou!
and no worries :)