Question

5. MEDICINE When doctors prescribe medication,

they have to consider the rate at which the body filters

a drug from the bloodstream. Suppose it takes the

human body 6 days to filter out half of the Flu-B-

Gone vaccine. The amount of Flu-B-Gone vaccine

remaining in the bloodstream x days after an injection

is given by the equation y = y(0.5), where y, is the

initial amount. Suppose a doctor injects a patient with

20 ug (micrograms) of Flu-B-Gone.

a. How much of the vaccine will remain after 1 day?

Round your answer to the nearest tenth.

b. How much of the vaccine will remain after 12 days?

Round your answer to the nearest tenth.

Answer 1

(i) 17.8 ug

(ii) 5 ug

Explanation:

The equation is given as :
`y=y_(0)(0.5)^(x/6)`

Initial Amount,
`y_(0)=20ug`

(a) After One Day i.e. x=1

Amount Left,
`y=y_(0)(0.5)^(x/6)=20(0.5)^(1/6)=20 X 0.8909 =17.8ug`

(b)After 12 days, x=12

Amount Left,
`y=y_(0)(0.5)^(x/6)=20(0.5)^(12/6)=20 X 0.25 =5ug`