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
zloy xaker [14]
3 years ago
6

The​ half-life of a certain tranquilizer in the bloodstream is 22 hours. How long will it take for the drug to decay to 90​% of

the original​ dosage? Use the exponential decay​ model, Upper A equals Upper A 0 e Superscript kt​, to solve.
Mathematics
1 answer:
nasty-shy [4]3 years ago
7 0

Answer:

It will take approximately 3.34 hours for the drug to decay to 90% of the original dosage

Step-by-step explanation:

As suggested, we use the formula for exponential decay:

A(t)=A_0\,e^{-k\,t}

From the given information, the half life of the drug in blood id 22 hours, so that means that it takes that number of hours to go from the initial value A_0, to a final value equal to A_0/2. Using this information we can find the decay rate "k" by solving for this parameter in the formula, and using the natural log function to bring the exponent down:

A(t)=A_0\,e^{-k\,t}\\\frac{A_0}{2} =A_0\,e^{-k\,*22}\\\frac{A_0}{A_0*2} =e^{-k\,*22}\\\frac{1}{2} =e^{-k\,*22}\\ln(\frac{1}{2})=-k\,*22\\ k=-\frac{ln(\frac{1}{2})}{22} \\k=0.0315

Now we use this value for the decay rate "k" to calculate how long it would take to decay to 90% of the original dose;

A(t)=A_0\,e^{-0.0315\,t}\\0.9*A_0} =A_0\,e^{-0.0315\,t}\\\frac{0.9*A_0}{A_0} =e^{-0.0315\,t}\\0.9 =e^{-0.0315\,t}\\ln(0.9)=-0.0315\,t\\ t=-\frac{ln(0.9)}{0.0315} \\t=3.3447\,hours

You might be interested in
What is the result when x4 – 723 – 13x2 – 2x + 7 is divided by x + 1? If there is
deff fn [24]
Can you post a picture please!
6 0
3 years ago
A company uses paper cups shaped like cones for its water cooler. Each cup has a height of 14cm, and the base has a radius of 3c
BlackZzzverrR [31]
16,493.75 is how much water
6 0
2 years ago
If an object weighs 120 pounds on earth how much will it way on mars
butalik [34]
The surface gravity of Mars is 3.7 m/s².  On Earth it is 9.8 m/s².  3.7/9.8 = 38%.

So 38% of 120 lbs is 45 pounds.
 
8 0
3 years ago
Write in slope-intercept form an equation of the line that passes through the given points. (5,4), (10,8)
professor190 [17]

Answer:

y=4/5x

Step-by-step explanation:

y=mx+b

plug in y and x into each equation and solve!

4=5m+b

8=10m+b

4=5m

m=4/5

b=0

y=4/5x+0

6 0
2 years ago
Joshua rolls two dice to form a two-digit
dusya [7]

Answer:

fits under statistics category (also probability or math :\)

4 0
3 years ago
Other questions:
  • Brice had 3 energy bars.he ate half of one.how many energy bars remained uneaten
    10·1 answer
  • Javier begins to save for a new bicycle that costs $415. He already has $140 and plans to save $25 per week. Let w represent the
    12·1 answer
  • The negation of " If it rains then the road is slippery"
    8·1 answer
  • Henry is putting money into a checking account. Let y represent the total amount of money in the account (in dollars). Let x rep
    9·1 answer
  • May you help me please?
    5·2 answers
  • It is a 375-mile drive from San Francisco to Los Angeles. A map scale shows 2 centimeters equaling 10 actual miles. How long is
    6·1 answer
  • What should be filled in the blank spot you’ll be marked as brainliest if you are correct
    13·1 answer
  • Which equations are true?<br> Choose All Answers That Apply (10 Points)
    15·2 answers
  • Which linear inequality is represented by the graph?
    11·1 answer
  • What is the range of this function?
    6·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!