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
zlopas [31]
2 years ago
5

If a person takes a prescribed dose of 10 milligrams of Valium, the amount of Valium in that person's bloodstream at any time ca

n be modeled with the exponential decay function A ( t ) = 10 e − 0.0188 t where t is in hours. a . How much Valium remains in the person's bloodstream 12 hours after taking a 10 -mg dose? Round to the nearest tenth of a milligram. mg b . How long will it take 10 mg to decay to 5 mg in a person's bloodstream? Round to two decimal places. hours c . At what rate is the amount of Valium in a person's bloodstream decaying 6 hours after a 10 -mg dose is taken. Round the rate to three decimal places.
Mathematics
1 answer:
aleksandr82 [10.1K]2 years ago
3 0

Answer:

(a)8.0mg

(b)36.87 hours

(c)-0.168

Step-by-step explanation:

The amount of Valium in that person's bloodstream at any time can be modeled with the exponential decay function A ( t ) = 10 e^{ -0.0188 t (t in hours)

(a)After 12 Hours

A ( 12) = 10 e^{ -0.0188*12}\\=7.98\\\approx 8.0 mg $(to the nearest tenth of a milligram)

(b)If A(t)=5mg

Then:

5= 10 e^{ -0.0188 t}\\$Divide both sides by 10\\0.5=e^{ -0.0188 t}\\$Take the natural logarithm of both sides\\ln (0.5)=-0.0188 t\\t=ln (0.5) \div (-0.0188)\\$t=36.87 hours (to two decimal places.)

(c)

A ( t ) = 10 e^{ -0.0188 t}\\A'(t)=10(-0.0188)e^{ -0.0188 t}\\A'(t)=-0.188e^{ -0.0188 t}\\$At 6 hours, the rate at which the amount of Valium is decaying therefore is:\\A'(6)=-0.188e^{ -0.0188*6}\\$=-0.168 ( to three decimal places)

You might be interested in
HELP ASAP <br><br> Find the zeros of y = x^2 - 4x - 9 by completing the square.
Alla [95]

Answer: x= 2 + √ 13 ,2- √ 13

Step-by-step explanation:

Replace y with 0 and solve for x

4 0
3 years ago
Read 2 more answers
What is a mathematical expression indicating to a root of a quantity?
vladimir1956 [14]
Find out smarty don’t cheat
7 0
2 years ago
The collection of all value is called the range of the function​
Phoenix [80]

Answer:

Step-by-step explanation:

False.  The range of a function is the set of all values taken on by the dependent variable ( e. g., by y in the set y = f(x) ).  By definition there is a single y value associated with each number (input) in the domain of the function.

4 0
3 years ago
Please helpp (exponents)
pshichka [43]

Answer:

the answer is 27

Step-by-step explanation:

for the show your work all you have to do is write 3x3x3=27

5 0
3 years ago
Tell whether the triangle with the given side lengths is a right triangle.
Lerok [7]

Answer:

No

Step-by-step explanation:

6 0
3 years ago
Other questions:
  • Help please thanks so much
    12·2 answers
  • Algebra 1 &gt; * 3.10 Solve linear equations: word problems UFG
    14·1 answer
  • What is the 6th factor in 42
    11·1 answer
  • For f(x)=4x+1 and g(x)=x^-5, find (f+g)(x)
    9·2 answers
  • What is 36 divided by 1/4 <br> PLS AWNSER ASAP
    9·2 answers
  • An online store holds a sale.Of the 500 customers who make a purchase during the sale,60 use a coupon.What percent of the custom
    6·2 answers
  • Given that B is the midpoint of segment AC. BC = 14x -26 and AB = 6x +6,<br> find the value of x.*
    15·1 answer
  • Zoey went to the store to buy some cherries. The price per pound of the cherries is
    8·1 answer
  • 9. If set A is a subset of set B, and set B is a subset of set C. Is it true that set A is a subset
    12·1 answer
  • 30 POINTS FOR THIS QUESTION
    5·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!