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
Rus_ich [418]
2 years ago
10

The antibiotic clarithromycin is eliminated from the body according to the formula A(t) = 500e−0.1386t, where A is the amount re

maining in the body (in milligrams) t hours after the drug reaches peak concentration. How much time will pass before the amount of drug in the body is reduced to 100 milligrams? (Round your answer to two decimal places.)
Mathematics
1 answer:
PolarNik [594]2 years ago
6 0

Answer:

Time(t) = 11.61 hours (Rounded to two decimal place)

Step-by-step explanation:

Given: The antibiotic  clarithromycin is eliminated from the body according to the formula:

A(t) = 500e^{-0.1386t}                 ......[1]

where;

A - Amount remaining in the body(in milligram)

t - time in hours after the drug reaches peak concentration.

Given: Amount of drug in the body is reduced to 100 milligrams.

then,

Substitute the value of A = 100 milligrams in [1] we get;

100= 500e^{-0.1386t}

Divide both sides by 500 we get;

\frac{100}{500}=\frac{ 500e^{-0.1386t}}{500}

Simplify:

\frac{1}{5} = e^{-0.1386t}

Taking logarithm both sides with base e, then we have;

\log_e (\frac{1}{5})= \log_e (e^{-0.1386t})

\log_e (\frac{1}{5})=-0.1386t         [ Using \log_e e^a =a ]

or

\log_e (0.2)=-0.1386t

-1.6094379124341 = -0.1386t

 [using value of \log_e (0.2) = -1.6094379124341 ]

then;

t = \frac{-1.6094379124341}{-0.1386}

Simplify:

t ≈11.61 hours.

Therefore, the time 11.61 hours(Rounded two decimal place) will pass before the amount of drug in the body is reduced to 100 milligrams


You might be interested in
Hhelp me pleaseeeeee
svetlana [45]

A. Area = ½b × h

= ½ × 16 × 9

= 72

B. Area = b × h

= 26 × 18

= 468

C. Area = a²

= 11²

= 121

D. Area = ½(a+b) × h

= ½(6+21) × 8

= 108


Hope this helps :)

Please consider marking my answer the brainliest!

4 0
3 years ago
What do you need to know?
bulgar [2K]

wym are you asking a question?

6 0
3 years ago
Read 2 more answers
What does y=5x+4 look like on slope intercept form?
valentina_108 [34]
Beachside it is supposed to be 619 into that form
4 0
3 years ago
Match the expression with its name.
enot [183]
Fourth-degree trinomial
4 0
3 years ago
Read 2 more answers
Variable expression for 3 times the sum of x and 2
Lynna [10]
3(x+2)
Remember in expressions there’s no equals sign
Hope this helps!!
6 0
3 years ago
Other questions:
  • I need help on what to do for part b
    7·1 answer
  • The temperature went from -12°F to 18°F. How much did the temperature change?
    14·1 answer
  • Which point represents -(-10) on the number line?
    5·1 answer
  • Write an equation for the line that is parallel to the glven line and that passes
    8·2 answers
  • Quick Answer Fast!!!!! five of the six tempstures for one day in june were 67, 72, 82, 79, and 80. If the mode of this data set
    14·1 answer
  • Let f (x)= x + 18 − 3 x − 15 Choose the correct interval form for the DOMAIN of f and then enter the values for the endpoint(s)
    15·1 answer
  • Can someone help please!!!!!!
    5·1 answer
  • Sanjay can travel 342 mi in 6 hours at this rate how far can he travel in 5 hours
    14·1 answer
  • 4x+7=64 i need the answer
    10·2 answers
  • The length is :____ meters and the width is ____meters.
    15·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!