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
7nadin3 [17]
3 years ago
7

Consider the spreading of a rumor through a company of 1000 employees, allworking in the same building.We assume that the spread

ing of a rumor is similar to the spreading of a contagious disease (see Example 3, Section 1.2) in that the number of people hearing the rumor each day is proportional to the product of the number who have heard the rumor previously and the number who have not heard the rumor. This is given by
rn+1 = rn + 1000krn(1000 ? rn)
where k is a parameter that depends on how fast the rumor spreads and n is the number of days. Assume k = 0.001 and further assume that four people initially have heard rumor. How soon will all 1000 employees have heard the rumor?
Mathematics
1 answer:
natima [27]3 years ago
5 0

Answer:

On the 12th day, the rumor would have has to all the 1000 employees

Step-by-step explanation:

Given the data in the question;

so, lets consider the rumor spreading thorough the company of 1000 employee;

the given model is; r_{n+1} = r_{n} + 1000kr_{n} ( 1000 - r_{n} )

where k is the parameter that depends on how fast the rumor spreads, n is the number of days.

now, lets assume k = 0.0001, lets also assume r₀ = 4

so to find how soon all 1000 employees  will have heard the rumor  ;

let n be;

then r1 will be;

r1 = r₀ + ( 0.001)r₀(1000-r₀ )

so

r1 = 4 + ( 0.001) × 4× (1000 - 4 )

r1 = 7.984

r2 will be;

r2 = r1 + ( 0.001)r1(1000-r1 )

r2 =  7.984 + ( 0.001) × 7.984 × (1000 - 7.984 )

r2 = 15.904255744

   

r3  will be;

r3 = r2 + ( 0.001)r2(1000-r2 )  

r3 = 15.904255744 + ( 0.001) × 15.904255744 × (1000 - 15.904255744 )

r3 = 31.555566137

Using the same formula and procedure by substituting n = 1,2,3,4,5,6,7,8,9,10,11,12.

we will have;

n        rₙ

0        4

1        7.984

2       15.904255744

3       31.555566137

4       62.1153785

5       120.372437

6       226.25535

7       401.319217

8       641.58132

9       871.53605

10     983.497013

11      999.727651

12     999.999926

Therefore, On the 12th day, the rumor would have has to all the 1000 employees

 

You might be interested in
BRANILIEST ANSWER GETS PICKED!
JulijaS [17]
The answer is 5 have a great day
4 0
2 years ago
Can some one help me with some math problems
Tatiana [17]
It's C, Y = 2x + 3. This is cause, if we use the table and say that y = 5 and x = 1, then 5 = 1 x 2 + 3 which is correct
4 0
3 years ago
Solve for y.<br> py + qy = -4y + 8<br> y =
Elanso [62]

Answer:

y=8/(p+q+4)

Step-by-step explanation:

py+qy=-4y+8

Collect all terms containing y together

Py+qy+4y=8

Factor out y

y(p+q+4)=8

Divide both sides by (p+q+4)

y(p+q+4)/(p+q+4)=8/(p+q+4)

y=8/(p+q+4)

3 0
3 years ago
Read 2 more answers
Solve the matrix equation for a, b, c, and d. [1 2] [a b] [6 5][3 4] [c d]= [19 8]
Anit [1.1K]

Answer:

The answer is "\bold{\left[\begin{array}{cc}a&b\\c&d\end{array}\right] = \left[\begin{array}{cc}7&-2\\ -\frac{1}{2}&\frac{7}{2}\end{array}\right]}".

Step-by-step explanation:

\bold{\left[\begin{array}{cc}1&2\\3&4\end{array}\right] \left[\begin{array}{cc}a&b\\c&d\end{array}\right] = \left[\begin{array}{cc}6&5\\ 19&8\end{array}\right]}

Solve the L.H.S part:

\left[\begin{array}{cc}1&2\\3&4\end{array}\right] \left[\begin{array}{cc}a&b\\c&d\end{array}\right]\\\\\\\left[\begin{array}{cc}a+2c&b+2d\\3a+4c&3b+4d\end{array}\right]

After calculating the L.H.S part compare the value with R.H.S:

\left[\begin{array}{cc}a+2c&b+2d\\3a+4c&3b+4d\end{array}\right]= \left[\begin{array}{cc}6&5\\ 19&8\end{array}\right]} \\\\

\to a+2c =6....(i)\\\\\to b+2d =5....(ii)\\\\\to 3a+4c =19....(iii)\\\\\to 3b+4d = 8 ....(iv)\\\\

In equation (i) multiply by 3 and subtract by equation (iii):

\to 3a+6c=18\\\to 3a+4c=19\\\\\text{subtract}... \\\\\to 2c = -1\\\\\to  c= - \frac{1}{2}

put the value of c in equation (i):

\to a+ 2 (- \frac{1}{2})=6\\\\\to a- 2 \times \frac{1}{2}=6\\\\\to a- 1=6\\\\\to a =6 +1\\\\\to a = 7\\

In equation (ii) multiply by 3 then subtract by equation (iv):

\to 3b+6d=15\\\to 3b+4d=8\\\\\text{subtract...}\\\\\to 2d = 7\\\\\to d= \frac{7}{2}\\

put the value of d in equation (iv):

\to 3b+4 (\frac{7}{2})=8\\\\\to 3b+4 \times \frac{7}{2}=8\\\\\to 3b+14=8\\\\\to 3b =8-14\\\\\to 3b = -6\\\\\to b= \frac{-6}{3}\\\\\to b= -2

The final answer is "\bold{\left[\begin{array}{cc}a&b\\c&d\end{array}\right] = \left[\begin{array}{cc}7&-2\\ -\frac{1}{2}&\frac{7}{2}\end{array}\right]}".

4 0
3 years ago
Jeremy loves snowboarding. His favorite stunt is catching big air and jumping off the ramp while holding on to the snowboard. Je
Georgia [21]
It has a slightly positive skew of 0.28
3 0
3 years ago
Other questions:
  • The Michigan veteran population in 1990 was 14.2% and in 2000 was 12.4%.
    5·1 answer
  • Nestor is saving money to buy a new camping tent each week he doubles the amount he saved the previous week if he saves a dollar
    15·1 answer
  • How many different breakfasts can you have at the local diner if you can select 3 different egg dishes​ (scrambled, fried,​ poac
    9·1 answer
  • Write the equation of a line that is perpendicular to x=3x=3x, equals, 3 and that passes through the point (0,-4)(0,−4)left pare
    6·1 answer
  • Help please! Identify m∠AMB. Pic attached below.
    15·2 answers
  • Use the graph to determine the input value for
    14·1 answer
  • Help!!!!!!!!!!!!!!!!!!!!!!!!!!
    7·2 answers
  • Need help plz on number 2
    15·1 answer
  • I need help quick- Thanks btw :&gt;
    11·1 answer
  • A+bx=z <br> get x by its self
    13·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!