1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
Snowcat [4.5K]
3 years ago
15

Suppose that you take 120 mg of an antibiotic every 4 hr. The​ half-life of the drug is 4 hr​ (the time it takes for half of the

drug to be eliminated from your​ blood). Use infinite series to find the​ long-term (steady-state) amount of antibiotic in your blood exactly.
Mathematics
1 answer:
vodomira [7]3 years ago
5 0

Answer:

The steady state amount of antibiotic in the bloodstream when t --> ∞ is 240 mg.

Step-by-step explanation:

Let the amount of antibiotic in one's bloodstream be given as Aₙ (where n = the number of half lives since the start of usage)

Let's follow the time line of events.

At t = 0 hr, the drug is taken

A₀ = 120 mg

At t = 4 hrs, n = 1, the drug is taken again

A₁ = (0.5×A₀) + 120

A₁ = (0.5×120) + 120 = 180 mg

At t = 8 hrs, n = 2, the drug is taken again,

A₂ = (0.5×A₁) + 120

A₂ = (0.5×180) + 120 = 210 mg

At t = 12 hrs, n = 3, the drug is taken again

A₃ = (0.5×A₂) + 120

A₃ = (0.5×210) + 120 = 225 mg

At this point, it becomes evident that at t = 4n hrs, n = n i.e. n half lives later, the general formula for the amount of the antibiotic in the bloodstream is

Aₙ = 0.5Aₙ₋₁ + 120

where Aₙ₋₁ = The amount of antibiotic in the bloodstream at the time t = 4(n-1) and (n-1) half lives later.

For infinite series, that are increasing in this order, as the value of n --> ∞,

Aₙ = Aₙ₋₁ = K

And our general formula becomes

K = 0.5K + 120

0.5K = 120

K = (120/0.5)

K = 240 mg

Hence, the steady state amount of antibiotic in the bloodstream when t --> ∞ is 240 mg.

Hope this Helps!!!

You might be interested in
To express a number in one unit as an equivalent value of another unit
ddd [48]
A conversion factor is a number used to change one set of units to another, by multiplying or dividing. When a conversion is necessary, the appropriate conversion factor to an equal value must be used. For example, to convert inches to feet, the appropriate conversion value is 12 inches equal 1 foot.
4 0
2 years ago
How to solve this please help!!
Angelina_Jolie [31]
Mary is incorrect. Perimeter is not proportional to area. An example which you can use is garden A is an 8 by 1 rectangle. The perimeter is 18 while the area is 8. Graden B is a 4 by 4 square. The perimeter is 16 (less than garden A) while the area is 16 (two times more than garden B). 
8 0
3 years ago
2800 ml +2.6 L<br> 2800 ml +2.6 L
Tom [10]

Answer:

10 800 ml

Step-by-step explanation:

I hope this helps :}

5 0
3 years ago
Which of the following statements incorrectly describes the line segment XY?
sveta [45]
Correct answer is C.

There are infinitely many possible paths between X and Y.
7 0
3 years ago
Solve 9 = 4 + x ( show your work )
Tanya [424]

Answer:

x = 5

Step-by-step explanation:

1. 9 = 4 + x

2. 9 - 4 = 4 + x - 4

3. 5 = x

4 0
3 years ago
Other questions:
  • In Detroit the high temperature in degrees Fahrenheit for five days in January were -12 , -8 , -3 , 6 , -15. What was the averag
    13·2 answers
  • Solve the following equation for b. 10a + 2b = 12
    12·2 answers
  • Mark eats an egg sandwich for breakfast and a big burger for lunch every day the egg sandwich has 250 calories if Mark has 5250
    5·1 answer
  • When two lines intersect, they form two pairs of vertical angles. If the measure of 21 is 60°, what is
    5·1 answer
  • WHATS 15 DIVIDE BY 6
    15·2 answers
  • After a 5% discount, a car is on sale for $11,400. What was the price of the car before the discount?
    15·2 answers
  • 10. Given the function below, what is f(3)?<br> f(x) = 2x2 - x-5
    13·1 answer
  • The price of a television is $700 at two different stores. Each store is offering a different promotion. Which deal is the best?
    5·2 answers
  • Each of the 90 fourth-grade students at North Elementary read 30 books over the school year.
    7·1 answer
  • Please Help! Will Give Brainlest!
    14·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!