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]
2 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]2 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
I need help I’m not sure
Daniel [21]

\bf ~~~~~~~~~~~~\textit{middle point of 2 points } \\\\ (\stackrel{x_1}{3}~,~\stackrel{y_1}{5})\qquad  (\stackrel{x_2}{-6}~,~\stackrel{y_2}{-6}) \qquad \left(\cfrac{ x_2 +  x_1}{2}~~~ ,~~~ \cfrac{ y_2 +  y_1}{2} \right) \\\\\\ \left( \cfrac{-6+3}{2}~~,~~\cfrac{-6+5}{2} \right)\implies \left(\cfrac{-3}{2}~~,~~\cfrac{-1}{2}  \right)\implies \left( -1\frac{1}{2}~,~-\frac{1}{2} \right)

3 0
3 years ago
Find the domain and range with a vertex of (1,-2)
klemol [59]

Answer:

see explanation

Step-by-step explanation:

the domain ( values of x ) that a quadratic can have is all real numbers

domain : - ∞ < x < ∞

the range ( values of y ) are from the vertex upwards , that is

range : y ≥ - 2

3 0
1 year ago
Passes through (3, 4) and (5, -4) how do I solve​
nikitadnepr [17]

Answer:

y = - 4x + 16

Step-by-step explanation:

Assuming you require the equation of the line passing through the points.

The equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

Calculate m using the slope formula

m = (y₂ - y₁ ) / (x₂ - x₁ )

with (x₁, y₁ ) = (3, 4) and (x₂, y₂ ) = (5, - 4)

m = \frac{-4-4}{5-3} = \frac{-8}{2} = - 4, thus

y = - 4x + c ← is the partial equation

To find c substitute either of the 2 points into the partial equation

Using (3, 4), then

4 = - 12 + c ⇒ c = 4 + 12 = 16

y = - 4x + 16 ← equation of line

8 0
3 years ago
Amrita bought a new delivery van for $32,500. The value of this van depreciates at a rate of 12% each year. Write a function f(x
FrozenT [24]

Answer:

The function, f(x) to model the value of the van can be expressed as follows;

f(x) = 32,500 \times \left(0.88\right)^x

Step-by-step explanation:

From the question, we have;

The amount at which Amrita bought the new delivery van, PV = $32,500

The annual rate of depreciation of the van, r = -12% per year

The Future Value, f(x), of the van after x years of ownership can be given according to the following formula

f(x) = PV \cdot \left(1 + \dfrac{r}{100} \right)^x

Therefore, the function, f(x) to model the value of the van after 'x' years of ownership can be expressed as follows;

f(x) = 32,500 \cdot \left(1 - \dfrac{12}{100} \right)^x = 32,500 \cdot \left(0.88\right)^x

8 0
3 years ago
Use the figure to complete the proportion.
MAVERICK [17]

Answer:

BE / AB = <u>HE</u> / AH

Step-by-step explanation:

AE is angle bisector

BE / HE = AB / AH

BE / AB = HE / AH

6 0
3 years ago
Other questions:
  • Help please explain as simple as possible
    12·1 answer
  • Connect A, B, and C to make a closed polygon.​
    8·1 answer
  • Alyssa,Keith,and Sally each have nine erasers.Alyssa has two pencils.how many erasers do they have have in all?
    9·2 answers
  • Help ASAP nowwwwwwwwwww
    10·1 answer
  • What is the equation of the line that passes through the points (-2, 3) and (2, 7)?
    14·1 answer
  • The value of 8 in 8,596 is how many times the value of 8 in 975?
    5·1 answer
  • Review the graph of y = sin(x). Based on the graph, what are the domain and range of the sine function? Y 3+ 2+ domain: [0, 2TT)
    15·1 answer
  • Let S be the set of all integers k such that, if k is in S, then <img src="https://tex.z-dn.net/?f=%5Cfrac%7B17k%7D%7B66%7D" id=
    9·1 answer
  • In ΔABC, where ∠C is a right angle, cos A=√21/5. What is sin B?
    7·1 answer
  • What is the cube root of 512m^12n^15
    15·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!