Question

Rick was given a prescription of antibiotics that were 500 milligram tablets. He was instructed to take 1 tablet a day. Suppose he had been taken the medicine for awhile (same time every day). The amount of medicine in his body (in milligrams) after n doses:
500+500(.3)+500(.3)^2+500(.3)^3+... +500(.3)^(n-1)
Find the amount of medicine that will be in his system if he follows doctor's orders. Round answer to nearest whole milligram.

Answer 1

714.28 ~ 714.3

Answer 2

I don't quite understand?

Answer 3

it basically forms a geometric progression

500 = a
r = .3


the summation of terms n of g.p is

1 - r^n
sum = a x ------
1 - r

Answer 4

now for the 1 - r^n

r = .3
n=500

r^n is very small so 1 - .3^500 ~ 1

so the formula for this question becomes sum = a/ ( 1 -r )

r = .3

1 - r = .7

sum = 500/.7 = 5000/7 ~ 714.3

Answer 5

do you understand now?

Answer 6

What does ~ stand for?

Answer 7

~ is for nearly equal to

Answer 8

like 7.47 = 7.47 ~ 7.5

Answer 9

So the amount of medicine would be ~ 714.3 milligrams?

Answer 10

yeah : )

Answer 11

Thank you so much ishaan! :)