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
Neko [114]
3 years ago
7

The monthly demand for a certain brand of perfume is given by the demand equation p = 100e−0.0002x + 125 where p denotes the ret

ail unit price (in dollars) and x denotes the quantity (in 1-oz bottles) demanded.
(a) Find the rate of change of the price per bottle when x = 2000 and when x = 3000. (Round your answers to four decimal places.)

x = 2000( ) dollars/bottle

x = 3000( ) dollars/bottle

(b) What is the price per bottle when x = 2000? When x = 3000? (Round your answers to the nearest cent.)

x = 2000 $ ( )

x = 3000 $ ( )
Mathematics
1 answer:
Fantom [35]3 years ago
3 0

Answer:

a)

Rate of change of the price per bottle when x = 2000

p'(2000)= -0.0134

Rate of change of the price per bottle when x = 3000

p'(3000)= -0.011

b)

Price per bottle when x = 2000

$192

Price per bottle when x = 3000

$180

Step-by-step explanation:

The equation of the demand x in terms of the price p is

\bf p(x)=100e^{-0.0002x}+125

(a) Find the rate of change of the price per bottle when x = 2000 and when x = 3000. (Round your answers to four decimal places.)

These are p'(x) at x=2000 and x=3000

\bf p'(x)=100(-0.0002)e^{-0.0002x}=-0.02e^{-0.0002x}

so

\bf p'(2000)=-0.02e^{-0.0002*2000}=-0.02e^{-0.4}=-0.0134

\bf p'(3000)=-0.02e^{-0.0002*3000}=-0.02e^{-0.6}=-0.011

(b) What is the price per bottle when x = 2000? When x = 3000? (Round your answers to the nearest cent.)

These are p(2000) and p(3000)

\bf p(2000)=100e^{-0.0002*2000}+125=100e^{-0.4}+125\approx 192

\bf p(3000)=100e^{-0.0002*3000}+125=100e^{-0.6}+125\approx 180

You might be interested in
Katy buys 4 DVDs every 2 weeks how many will she buy in 10
malfutka [58]

If she maintains her average amount of movies bought every week, then she will buy 20 DVDs in 10 weeks. Explanation: she buys 4 every week, so if we want to find out how many are in 10 weeks, we must multiply two until we get to 10 ( five weeks ) then multiply that buy her average of movies. And that is how we get the answer of 20 DVDs! ( her at least I did )

Anyways, hope this helps!

5 0
3 years ago
Read 2 more answers
What is the value? <br><br> -8 * 2/3
Slav-nsk [51]

Answer: -5 2/3

Step-by-step explanation:

6 0
3 years ago
1-3. Find the center point, the radius and the diameter for the following equation: x² + y2 = 16
kogti [31]

Answer:

Center: (0, 0)

Radius: 4

Step-by-step explanation:

Circle Standard Equation: (x - h)² + (y - k)² = r²

(h, k) is center

r is radius

We see that our <em>h</em> and our <em>k</em> are both 0.

∴ Our center is (0, 0), origin.

We see that our r² = 16

√r² = √16

∴ Our radius is equal to 4

3 0
3 years ago
Triangle ABC is similar to triangle XYZ. fine side a
aleksley [76]
<h3>Answer:  a = 15</h3>

Explanation:

The jump from 13 to 39 is "times 3" when comparing the diagonal segments. So the jump from 5 to 'a' must also be "times 3" to keep the sides in the same proportion. Therefore, a = 3*5 = 15.

Or we could solve it like so

13/39 = 5/a

13a = 39*5 ... cross multiplying

13a = 195

a = 195/13 .... dividing both sides by 13

a = 15

4 0
2 years ago
Find the slope and​ y-intercept of the line whose equation is 2 x plus y equals 3 (2x+y=3).
jolli1 [7]
You can solve this equation by rearranging the 2x to the opposite side, but since it's a positive, you must change it to a negative. If the number was negative, it would've been a positive.
y=-2x+3
-2x is the slope and 3 is the y-intercept.
Hope this helped!
8 0
3 years ago
Other questions:
  • PART A: Mrs. konsdorf claims that angle R is a right angle.Is Mrs. konsdorf correct? explain your reasoning PART B: if T is trab
    13·1 answer
  • Are these triangles similar<br><br> Please hurry!
    13·2 answers
  • A total of 200 video game players take a survey on their favorite game. Unknown kingdom get 55% of votes. the video game designe
    9·1 answer
  • The area of an Equilateral triangle is given by the formula A= 3pi squared/4(s)Squared. Which formula represents the length of e
    5·1 answer
  • How do you write 11/ 4 as a percentage?
    8·1 answer
  • Solutions to ( x - 2 )² = -16​
    10·2 answers
  • −5 − 5/3 =<br> solve this right and get points!
    9·2 answers
  • State if the triangles in each pair are similar. If so, state how you know they are similar
    5·1 answer
  • Solve the question: 4/5 (b-1)-1/b=1
    11·1 answer
  • 20+30+20.13 what is it
    14·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!