Find the difference 0.2−0.05

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

zmey [24]

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.

8 0

3 years ago

Power Series Differential equation

KatRina [158]

The next step is to solve the recurrence, but let's back up a bit. You should have found that the ODE in terms of the power series expansion for $y$

$\displaystyle\sum_{n\ge2}\bigg((n-3)(n-2)a_n+(n+3)(n+2)a_{n+3}\bigg)x^{n+1}+2a_2+(6a_0-6a_3)x+(6a_1-12a_4)x^2=0$

which indeed gives the recurrence you found,

$a_{n+3}=-\dfrac{n-3}{n+3}a_n$

but in order to get anywhere with this, you need at least three initial conditions. The constant term tells you that $a_2=0$ , and substituting this into the recurrence, you find that $a_2=a_5=a_8=\cdots=a_{3k-1}=0$ for all $k\ge1$ .

Next, the linear term tells you that $6a_0+6a_3=0$ , or $a_3=a_0$ .

Now, if $a_0$ is the first term in the sequence, then by the recurrence you have

$a_3=a_0$
$a_6=-\dfrac{3-3}{3+3}a_3=0$
$a_9=-\dfrac{6-3}{6+3}a_6=0$

and so on, such that $a_{3k}=0$ for all $k\ge2$ .

Finally, the quadratic term gives $6a_1-12a_4=0$ , or $a_4=\dfrac12a_1$ . Then by the recurrence,

$a_4=\dfrac12a_1$
$a_7=-\dfrac{4-3}{4+3}a_4=\dfrac{(-1)^1}2\dfrac17a_1$
$a_{10}=-\dfrac{7-3}{7+3}a_7=\dfrac{(-1)^2}2\dfrac4{10\times7}a_1$
$a_{13}=-\dfrac{10-3}{10+3}a_{10}=\dfrac{(-1)^3}2\dfrac{7\times4}{13\times10\times7}a_1$

and so on, such that

$a_{3k-2}=\dfrac{a_1}2\displaystyle\prod_{i=1}^{k-2}(-1)^{2i-1}\frac{3i-2}{3i+4}$

for all $k\ge2$ .

Now, the solution was proposed to be

$y=\displaystyle\sum_{n\ge0}a_nx^n$

so the general solution would be

$y=a_0+a_1x+a_2x^2+a_3x^3+a_4x^4+a_5x^5+a_6x^6+\cdots$
$y=a_0(1+x^3)+a_1\left(x+\dfrac12x^4-\dfrac1{14}x^7+\cdots\right)$
$y=a_0(1+x^3)+a_1\displaystyle\left(x+\sum_{n=2}^\infty\left(\prod_{i=1}^{n-2}(-1)^{2i-1}\frac{3i-2}{3i+4}\right)x^{3n-2}\right)$

4 0

3 years ago

A airplane traveled 120 km in 240 minutes. What is the average speed of the airplane? a. 40 b. 10 C. 30 d. 60

Solnce55 [7]

Answer:

C

Step-by-step explanation:

240m= 4h

120km

V= 120/4 = 30 km/h

I hope this helps, have a good day

4 0

3 years ago

7 divide by k in algebric expression

Salsk061 [2.6K]

7 devide by k in algebric function = 7/k

4 0

3 years ago

The number 49 has two square roots: 7 and _____

Ainat [17]

Answer:

-7

Step-by-step explanation:

Square numbers always have two possible roots: a positive and negative root. This is because two positive numbers multiply to make a positive number and two negative numbers also multiply to make a positive number

-7 × -7 is still 49, just like 7 × 7

Hope this helps!

4 0

3 years ago

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