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
Semenov [28]
3 years ago
11

Suppose that, for a particular social networking company, the annual revenue from rich media advertisements, in millions of doll

ars, for the years 2007 through 2012 can be approximated with the model R ( x ) = − x^4 + 8 x^3 − 38 x^2 + 44x , where x is the number of years from the beginning of 2007.
a. For this company, what was the revenue from rich media advertisements at the beginning of 2010?

B. At what rate was the revenue changing in the year 2010?
Mathematics
1 answer:
Juli2301 [7.4K]3 years ago
8 0

Answer:

a. Revenue of the company at the beginning of 2010 is 75 million dollar (loss)

b. Rate at which the revenue changing in the year 2010 is 76 million dollar per year ( decreasing)

Step-by-step explanation:

For part a,

Given that x is the number of years at the beginning of 2007.

Therefore, x=0 for year 2007.

Hence at the year 2010 value of x will be x=3.

Substitute the value of x=3 in R(x),

R\left(x\right)=-x^{4}+8x^{3}-38x^{2}+44x

R\left(x\right)=-\left(81\right)+8\left(27\right)-38\left(9\right)+132

R\left(x\right)=-81+216-342+132

R\left(x\right)=-75

Negative sign indicates that there is loss of revenue at the start of the year 2010

Therefore, there is loss of revenue at the beginning of 2010 which is 75 million dollar.

For part b,

To calculate rate, differentiate the given function with respect to x.

\dfrac{d}{dx}R\left(x\right)=\dfrac{d}{dx}\left (-\left(x\right)^{4}+8\left(x\right)^{3}-38\left(x\right)^{2}+44\left(x\right)\right)

Applying sum and difference rule of derivative,

\dfrac{d}{dx}R\left(x\right)=-\dfrac{d}{dx}\left(x^4\right)+\dfrac{d}{dx}\left(8x^3\right)-\dfrac{d}{dx}\left(38x^2\right)+\dfrac{d}{dx}\left(44x\right)

Applying constant multiple rule of derivative,

\dfrac{d}{dx}R\left(x\right)=-\dfrac{d}{dx}\left(x^4\right)+8\dfrac{d}{dx}\left(x^3\right)-38\dfrac{d}{dx}\left(x^2\right)+44\dfrac{d}{dx}\left(x\right)

Applying power rule of derivative,

\dfrac{d}{dx}R\left(x\right)=-\left(4x^{4-1}\right)+8\left(3x^{3-1}\right)-38\left(2x^{2-1}\right)+44\left(1x^{1-1}\right)

\dfrac{d}{dx}R\left(x\right)=-4\left(x^{3}\right)+8\left(3x^{2}\right)-38\left(2x^{1}\right)+44

\dfrac{d}{dx}R\left(x\right)=-4x^3+24x^2-76x+44

Substituting the value x=3,

\dfrac{d}{dx}R\left(x\right)=-4\left(3\right)^3+24\left(3\right)^2-76\left(3\right)+44

\dfrac{d}{dx}R\left(x\right)=-4\left(27\right)+24\left(9\right)-76\left(3\right)+44

\dfrac{d}{dx}R\left(x\right)=-108+216-228+44

\dfrac{d}{dx}R\left(x\right)=-76

Negative sign indicates that rate is decreasing.

Rate at which the revenue is changing in the year 2010 is 76 million dollar per year.

You might be interested in
Which expression is equivalent to ( 4mn / m^-2n^6)^-2
inn [45]

Here are a few rules with exponents that apply here:

  1. Raising a power to a power: (x^m)^n=x^{m*n}
  2. Dividing exponents of the same base: \frac{x^m}{x^n}=x^{m-n}
  3. Converting negative exponents to positive ones: x^{-m}=\frac{1}{x^m}\ \textsf{and}\ \frac{1}{x^{-m}}=x^m

Firstly, solve the outer exponent:

(\frac{4mn}{m^{-2}n^{6}})^{-2}=\frac{4^{-2}m^{-2}n^{-2}}{m^{-2*-2}n^{6*-2}}=\frac{4^{-2}m^{-2}n^{-2}}{m^4n^{-12}}

Next, divide:

\frac{4^{-2}m^{-2}n^{-2}}{m^4n^{-12}}=4^{-2}m^{-2-4}n^{-2-(-12)}=4^{-2}m^{-6}n^{10}

Next, convert the negative exponents:

4^{-2}m^{-6}n^{10}=\frac{n^{10}}{4^2m^6}=\frac{n^{10}}{16m^6}

<u>Your final answer is n^10/16m^6 , or B.</u>

8 0
3 years ago
A tiny songbird called the blackpoll warbler migrates each fall from North America. A tracking study showed one bird flew from V
Alexus [3.1K]

Answer:

<h3>2642km</h3>

Step-by-step explanation:

Given the map coordinates o a bird during travel from Vermont at cordinate (63,45) toto Venezuela at map coordinates (67,10). In order to know how far the bird has travelled, we need to find the distance between the two coordinates first using the formula;

D = \sqrt{(x_2-x_1)^2+(y_2-y_1)^2}

Given x₁ = 63, y₁ = 45, x₂ = 67, y₂ = 10

D =\sqrt{(67-63)^2+(10-45)^2}\\ \\D = \sqrt{4^2+(-35)^2} \\\\D = \sqrt{16+1225} \\\\D = \sqrt{1241} \\\\D = 35.2278

If each map coordinate represents 75 kilometers, then the birds distance in km will be 75*35.2278 = 2642.087km

Hence the birds distance in km will be 2642km to the nearest kilometers

4 0
2 years ago
Cheryl pays $69 for 6 DVDs.  
yanalaym [24]
$69 ÷ 6 = 11.5 per DVD
11.5 × 4 = 46
7 0
3 years ago
Read 2 more answers
X + 3= -x -5<br><br>what's x?​
Karo-lina-s [1.5K]

Answer:

-4

Step-by-step explanation:

4 0
2 years ago
Read 2 more answers
What does it mean to the rise over run when the slope is an integer?
Brilliant_brown [7]

Answer: I think it’s C.

sorry if it’s wrong❣️.

8 0
3 years ago
Other questions:
  • Supriya and Sanya are huge fans of Tazo cards. Supriya has a lot more cards than Sanya and is willing to give her
    13·1 answer
  • The cost to replace a water pump in a car was $823. This included $383 for the water pump and $88 per hour for labor. How many h
    5·1 answer
  • Answer is all I need you’ll get 15 points if it is right
    13·1 answer
  • Last weekend Mandy collective four times as many shows as Cameron. Together they collected 40 shells. How many shells dkd Mandy
    14·2 answers
  • If f(x) equals 3X -2 what is f(5.9)
    8·1 answer
  • Will multiplying 3.14 by a fraction result in a rational answer
    11·1 answer
  • Need answer ASAP giving 10 points
    6·1 answer
  • Here is a table of values for y=f(x). Mark the statements that are true.
    6·1 answer
  • a positive number of two digits the ten place exced.the unit place digit by 5 .if the producted digit is 46. find the number​
    15·1 answer
  • A warehouse floor has a perimeter of 4,614 yards. What is the perimeter of<br> the floor in feet?
    9·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!