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
Luden [163]
2 years ago
15

Scenario: Two people in a major city with a population of 450,000 get infected with a rapidly spreading virus. If each day the i

nfected person infects 2 additional people, do the following:
1) Create a table with two columns. The first column should be labeled as "Number of Days" and the second column "TOTAL Number People Infected." Fill in the table for days 0 through 5.
2) Using the data from the table created in step 1, create a graph with "Number of Days" on the x-axis and "Total Infected People" on the y- axis.
3) Create a mathematics model (the equation) for this scenario.
4) How long will it take the ENTIRE city to be infected (Round to 2 decimal) places?

Mathematics
1 answer:
zmey [24]2 years ago
8 0

1) See attachment.

2) See attachment

3) y=2^{x+1}

4) 17.8 days

Step-by-step explanation:

1)

The table is in attachment.

In this problem, we are told that the initial number of people infected ad day zero is two, so the first row is (0,2).

Then, we are told that each day, an infected person infects 2 additional people. Therefore, at day 1, the number of infected people will be 2*2=4.

Then, each of the 4 persons infect 2 additional persons, so the number of infected people at day 2 will be 4*2=8.

Continuing the sequence, the following days the number of infected people will be:

8*2 = 16

16*2 = 32

32*2 = 64

2)

The graph representing the situation is shown in attachment.

On the x-axis, we have represented the day, from zero to 5.

On the y-axis, we have represented the number of infected people.

We see that the points on the graph are:

0, 2

1, 4

2, 8

3, 16

4, 32

5, 64

3)

Here we have to create a mathematics model (so, an equation) representing this scenario.

First of all, we notice that the number of infected people at day 0 is 2:

p(0)=2

To write an equation, we call x the number of the day; this means that at x = 0, the value of y (number of infected people) is 2:

y=2

Then, at day 1 (x=1), the number of infected people is doubled:

y(1)=2y(0)=2\cdot 2 = 4

And so on. This means that for each increase of x of 1 unit, the value of y doubles: so, we can represents the model as

y=2\cdot 2^x

Or

y=2^{x+1}

4)

Here we are told that the entire city has a population of

p = 450,000

people.

In order for the virus to infect the whole population, it means that the value of y must be equal to the total population:

y = 450,000

Substituting into the equation of the model, this means that

450,000 = 2^{x+1}

And solving for x, we find the number of days after which this will happen:

log_2(450,000)=x+1\\x=log_2(450,000)-1=17.8 d

So, after 17.8 days.

You might be interested in
Please help me out! :)
skad [1K]
3x-11=x+23
-x -x
2x-11=23
+11 +11
2x=34
x=17

3(17)-11 17+23
=40 =40

explanation ;
you would equal them because they are congruent . & you substitute x for 17 in each equation to find out the degrees of both of the angles :)

8 0
3 years ago
Which ordered pair (x, y) is the solution to the given system of linear equations?
anygoal [31]

Answer:

(-1,0)

Step-by-step explanation:

3(-1)+3(0)=-3

-3+0=-3

-3=-3

-2(-1)+(0)=2

2+0=2

2=2

4 0
3 years ago
Joe saves most of his allowance every week since his 7birthday. If joe saves $4 per week, how much money would he have saved on
maksim [4K]

Answer:

multiply

Step-by-step explanation:

7x 15= 105

105x4=420

then add 105+420= 44,100

6 0
3 years ago
Read 2 more answers
Find the assessed value of a home with a market value of 88,000 if the assessement rate is 42%
dolphi86 [110]

(0.42)(88000)=36,960

8 0
3 years ago
1.4 km =<br> 140m<br> 1400m<br> 14m<br> d<br> 14000m
Usimov [2.4K]

Answer:140 meters

Step-by-step explanation:1km=100m, 1.4km times 100=140

6 0
2 years ago
Read 2 more answers
Other questions:
  • 45% of the fish in a shop is marlin. The remainder is dolphin. If there are 110 dolphins how many marlin are in the shop ?
    6·2 answers
  • Is -3.7 less than,greater than or equal to -3.8 ?<br>​
    6·1 answer
  • The liver and esophagus are part of the digestive system. True or False
    12·2 answers
  • Which inequality best represents that ice cream at −5°C is cooler than ice cream at 4°C?
    8·1 answer
  • Is rolling doubles a simple event or compound event? Explain.<br><br><br> (rolling double dice)
    13·2 answers
  • One serving of scrambled eggs contains 7.8 grams of fat. Mr.Jensen is trying to eat no more than 60 grams of fat per day.if he e
    11·1 answer
  • Svp je veux une aide avec la question n°2 de l'exercice n°3
    13·1 answer
  • A craft show has an admission fee of $1.50 for children and $4.00 for adults. On Saturday 155 people came to the carnival and $5
    11·1 answer
  • Explain why y = 3x IS an exponential function and y = x3 is NOT an exponential function.
    9·1 answer
  • What is the surface area?
    14·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!