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 a certain vaccine.

Question

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 a certain vaccine. The amount of the vaccine remaining in the bloodstream x days after an injection is given by the equation y=y₀(0.5)^x/6, where y₀ is the initial amount. Suppose a doctor injects a patient with 20 μg (micrograms) of the vaccine.

 

a. How much of the vaccine will remain after 1 day? Round your answer to the nearest tenth.

 

 ____μg

 

b. How much of the vaccine will remain after 12 days? Round your answer to the nearest tenth, if necessary.

 

____ μg

 

c. After how many days will the amount of vaccine be less than 1 μg?.

 

after ____ days

Answer 1

a)  y=y₀(0.5)^x/6 We are looking for y, so y = 20 ug x 0.5^1/6. Use the y^x function to calculate 0.5^1/6.

y = 17.8 ug.

b) y = 20 x 0.5^12/6 = 5 ug.

c)  y=y₀(0.5)^x/6, so 1 = 20 x 0.5^x/6. We need to evaluate this for x. Take the logarithm of both sides of the equation

log 1 = log20 + x/6 log 0.5

0 = 1.30 + x/6 x -0.3. Solving for x gives 26. It should take greater than 26 days to get less than 1 ug.

Answer 2

Hi Elo H

Since you are given a formula to follow and information to plug into that formula you can just use it as follows:

y = y₀(0.5)^x/6

Where

y₀ = initial amount = 20

x = number days

For a you plug in the numbers and do the calculation

y = 20(0.5)^1/6

For b you plug in the numbers and do the calculation

y = 20(0.5)^12/6

The information given also says that it takes the human body 6 days to filter out half the medication. If you start with 20 µg, after 6 days you have 10µg it would follow that after 12 days you should half of 10. Can you complete the calculation above to confirm this.

For c you would use logarithms to find the exponent x

You can check the formula given with the information given

y = y₀(0.5)^x/6

Check your given information

y₀ = 20

x = 6

y = 20(0.5)^6/6 = 20(0.5) = 10

y = 10µg half the amount of vaccine that was initially injected.

I hope you find this useful.