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
lyudmila [28]
3 years ago
7

After an antibiotic tablet is taken, the concentration of the antibiotic in the bloodstream is modelled by the function C(t)=8(e

^(-0.4t)-e^(-0.6t)) where the time t is measured in hours and C is measured in mewg/mL.
What is the maximum concentration of the antibiotic during the first 12 hours?
Mathematics
1 answer:
Alexxx [7]3 years ago
4 0

Answer:

the maximum concentration of the antibiotic during the first 12 hours is 1.185 \mu g/mL at t= 2 hours.

Step-by-step explanation:

We are given the following information:

After an antibiotic tablet is taken, the concentration of the antibiotic in the bloodstream is modeled by the function where the time t is measured in hours and C is measured in \mu g/mL

C(t) = 8(e^{(-0.4t)}-e^{(-0.6t)})

Thus, we are given the time interval [0,12] for t.

  • We can apply the first derivative test, to know the absolute maximum value because we have a closed interval for t.
  • The first derivative test focusing on a particular point. If the function switches or changes from increasing to decreasing at the point, then the function will achieve a highest value at that point.

First, we differentiate C(t) with respect to t, to get,

\frac{d(C(t))}{dt} = 8(-0.4e^{(-0.4t)}+ 0.6e^{(-0.6t)})

Equating the first derivative to zero, we get,

\frac{d(C(t))}{dt} = 0\\\\8(-0.4e^{(-0.4t)}+ 0.6e^{(-0.6t)}) = 0

Solving, we get,

8(-0.4e^{(-0.4t)}+ 0.6e^{(-0.6t)}) = 0\\\displaystyle\frac{e^{-0.4}}{e^{-0.6}} = \frac{0.6}{0.4}\\\\e^{0.2t} = 1.5\\\\t = \frac{ln(1.5)}{0.2}\\\\t \approx 2

At t = 0

C(0) = 8(e^{(0)}-e^{(0)}) = 0

At t = 2

C(2) = 8(e^{(-0.8)}-e^{(-1.2)}) = 1.185

At t = 12

C(12) = 8(e^{(-4.8)}-e^{(-7.2)}) = 0.059

Thus, the maximum concentration of the antibiotic during the first 12 hours is 1.185 \mu g/mL at t= 2 hours.

You might be interested in
HELP ME PLEASE! 30 POINTS
bazaltina [42]

Answer:

C=14

Step-by-step explanation:

To find the minimum value, graph each of the inequalities. After graphing each inequality, test a point and shade the region that satisfies the inequality. Once all inequalities have been shaded, find the region where they all overlap. The region will be bounded by intersection points. Test each of these points into C=x+3y. The least value for C is the minimum.

(14,0)                  (0,17.5)                   (3.08,3.64)

C=14+3(0)           C=0+3(17.5)           C=3.08 + 3(3.64)

C=14                   C=52.5                   C=14

8 0
3 years ago
Read 2 more answers
What is the coefficient of x2 in this trinomial?
podryga [215]

Answer:

The coefficient is 1

Step-by-step explanation:

There is an imaginary 1 in front of variables that becomes the coefficient if there isn't already a number there. If it was 5x squared, the coefficient would be 5.

4 0
2 years ago
The length of a rectangle exceeds its breadth by 7cm. if the length is decreased by 4cm and the breadth is increased by 3cm, the
riadik2000 [5.3K]

Answer:

16cm

Step-by-step explanation:

Let the breadth = x

The length exceeds = x + 7

The breadth increased = x + 3

Because it said the length decreased by 4 so, the length would be:

x + 7 - 4 = x + 3

Original area:

We learn that:

area = length * breadth

x*(x+7) = (x+3)*(x+3)

x^2 + 7x = (x+3)^2

x^2 + 7x = x^2 + 6x + 9 (We also learn that (a+b)^2 = a^2 + 2ab + b^2

x^2 - x^2 + 7x - 6x = 9

x = 9 (so the breadth = 9)

The length = x + 7 = 9+7 = 16(cm)

Hope this help you :3

7 0
3 years ago
How do you convert kilometers to meters
NARA [144]

Answer:

1 kilometer is 1000 meters, so you multipy 1000 meters by the number of kilometers.

Step-by-step explanation:

1 kilometer = 1000 meters

<em>Hope this helped!!!! =)</em>

8 0
3 years ago
What is equivalent to 40/64
Nadya [2.5K]

Answer: 5/8


Step-by-step explanation:


8 0
3 years ago
Other questions:
  • It took Joe 3 hours swimming at a speed of 12 miles per hour to swim along the Charles River. If Jennifer is swimming the same p
    5·2 answers
  • Hat is the greatest common factor of 20 and 36? 2 4 5 6
    7·1 answer
  • Given f(x) = 3x - 1 and g(x)= -x + 6, find f(-2) + g(5).
    9·2 answers
  • At your summer job, you make $500 per month plus a commission of $2.75 on every item you sell. If you sold 145 items last month,
    14·1 answer
  • Tell the numbers that are odd and prime 2,14,23,24,25,31,45
    9·2 answers
  • The factorization of x2 + 3x – 4 is modeled with algebra tiles. What are the factors of x2 + 3x – 4?
    7·2 answers
  • 2.03-4.60 PLEASE HELP ME
    14·1 answer
  • Factor each polynomial <br> -28y^2-12y^5
    7·1 answer
  • Find the area of the circle. Round your answer to the nearest hundredth.
    6·1 answer
  • A number rounded to the nearest hundred thousand is 400,000 the same number rounded to the nearest ten thousand is 350,000 what
    14·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!