Suppose a rumor is going around a group of 191 people. Initially, only 38 members of the group have heard the rumor, but 3 days later 68 people have heard it. Using a logistic growth model, how many people are expected to have heard the rumor after 6 days total have passed since it was initially spread? (Round your answer to the nearest whole person.)

Answers

Answer 1

Answer:

106 people.

Step-by-step explanation:

Logistic equation:

The logistic equation is given by:

[tex]P(t) = \frac{K}{1+Ae^{-kt}}[/tex]

In which

[tex]A = \frac{K - P_0}{P_0}[/tex]

K is the carrying capacity, k is the growth/decay rate, t is the time and P_0 is the initial value.

Suppose a rumor is going around a group of 191 people. Initially, only 38 members of the group have heard the rumor.

This means that [tex]K = 191, P_0 = 38[/tex], so:

[tex]A = \frac{191 - 38}{38} = 4.03[/tex]

Then

[tex]P(t) = \frac{191}{1+4.03e^{-kt}}[/tex]

3 days later 68 people have heard it.

This means that [tex]P(3) = 68[/tex]. We use this to find k.

[tex]P(t) = \frac{191}{1+4.03e^{-kt}}[/tex]

[tex]68 = \frac{191}{1+4.03e^{-3k}}[/tex]

[tex]68 + 274.04e^{-3k} = 191[/tex]

[tex]e^{-3k} = \frac{191-68}{274.04}[/tex]

[tex]e^{-3k} = 0.4484[/tex]

[tex]\ln{e^{-3k}} = \ln{0.4484}[/tex]

[tex]-3k = \ln{0.4484}[/tex]

[tex]k = -\frac{\ln{0.4484}}{3}[/tex]

[tex]k = 0.2674[/tex]

Then

[tex]P(t) = \frac{191}{1+4.03e^{-0.2674t}}[/tex]

How many people are expected to have heard the rumor after 6 days total have passed since it was initially spread?

This is P(6). So

[tex]P(6) = \frac{191}{1+4.03e^{-0.2674*6}} = 105.52[/tex]

Rounding to the nearest whole number, 106 people.


Related Questions

What are the x-intercepts for the function ƒ(x) = -x(x − 4)?
A 0
B -1, 4
C 4
D 0, 4

What are the solutions to the quadratic equation 4x2 − x − 3 = 0?

Answers

Answer:

D

Step-by-step explanation:

f(x)=-x(x-4)

f(x)=-x²+4x

-x²+4x=0

x(-x+4)=0

x=0, x=4

(2)

4x²-x-3=0

(4x²+3x)-(4x-3)=0

x(4x+3)-1(4x+3)=0

x=1, x=-3/4

I need the answer explained

Answers

Answer:

1.33

Step-by-step explanation:

62 can only be subtracted from 82 once. So 82.46-62 would be 20.46. Since you can't subtract anymore you put a decimal point. 62x3=186 and 20.46-186=1.86 and you can subtract 186-186=0.

Help me please and thank you

Answers

Step-by-step explanation:

jlejej

are u using chrome os

Log 1 with whatever base (except 0) is 0 for any number (except 0) raised to 0th power is 1. And 0 times anything is 0. Answer should be B.

Nhà trường muốn đánh giá tỉ lệ chăm học của sinh viên (trong một tuần). Khảo sát 236 sinh viên thì thấy có 32 sinh viên chăm học. Hãy ước lượng khoảng đối xứng cho tỉ lệ sinh viên chăm học của trường với độ tin cậy 95%

Answers

Answer:

can't understand the language

Please Answer This!!! I NEEEDDD TOOO KNOWWWWW ANSWER!!!

Answers

Answer:

77.5

Step-by-step explanation:

Its rising at a constant rate between +10-15 each hour, so we if we were to add 25 or so to the 50, it would be close to 77.5, so I would assume the answer was B

1. In the past, Sam cashed his paycheck each month at Ready Cash, a check cashing service that
charges a 5% fee. He recently opened a checking account at Bank of America so he can now
deposit and/or cash his paycheck without a fee. If Sam is making $28,500 per year, how much will
he save by not going to Ready Cash anymore?

Answers

Step-by-step explanation:

28000 ÷ 100

=280

280 × 5

=1400

4. Lynn can walk two miles intenta
24 minutes. At this rate, how long will
it take her to walk 6 miles?

Answers

Lynn will take 1 hour and 12 minutes to walk
6 miles.

PLEASE HELP!!!
Evaluate each expression.
(252) =

Answers

Answer:

1/5

Step-by-step explanation:

A normal distribution has a mean of 20 and a standard deviation of 4. Determine the z-score for the data value of 42.

Answers

Answer:

Z = (42-20)/4 = 5.5

Z = X-μ / σ

Step-by-step explanation:

The z-score for the data value of 42 is 5.5.

What is a z-score?

A z-score is defined as the fractional representation of data point to the mean using standard deviations.

Formula of z-score = (X - μ) / σ

Given,

μ = 20

σ = 4

X = 42

z-score = (X - μ) / σ

Substitute the values,

z-score =  (42-20)/4

z-score = 22/4

z-score =  5.5

Hence, the z-score for the data value of 42 is 5.5.

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Help please!??!!?!?

Answers

9514 1404 393

Answer:

  a) CP = SP/1.1

  b) CP = $59.50

  c) GST = $5.95

Step-by-step explanation:

a) Divide by the coefficient of CP.

  SP = 1.1×CP

  CP = SP/1.1

__

b) Use the formula with the given value.

  CP = $65.45/1.1 = $59.50

__

c) You can do this two ways: subtract CP from SP, or multiply CP by 0.1.

  GST = SP -CP = $65.45 -59.50 = $5.95

  GST = CP×0.10 = $59.50 × 0.10 = $5.95

Please help explanation if possible

Answers

Answer:

N=18

Step-by-step explanation:

Hope it will help you

If it does pls give me Brainlest

Have a nice day

Answer:

18

Step-by-step explanation:

use the concept of similarity and enlargement.

[tex] \frac{15}{n} = \frac{5}{6 } [/tex]

[tex]n = \frac{15 \times 6}{5} [/tex]

[tex]n = 18[/tex]

could anyone help me solve this? I’ve had several questions like this and I don’t understand how to solve it. I’ll give brainliest:)

Answers

Answer:

-2, - 1, - 2 and - 3

Step-by-step explanation:

As the graph depicts an odd function, it will follow the rule f(-x) = - f(x)

what song goes whoooooo Iiiiii smoooooooooke ​

Answers

Answer:

Lol yu lateee das "who i smoke by yung ace"

Step-by-step explanation:

Answer:

woogle said woo hoo  by rock a teens

Step-by-step explanation:

if a stone is dropped from a cliff that is 122.5m high then its height in meters after t seconds is h=122.5-4.9t^2. find its velocity after 2s

Answers

Answer:

Step-by-step explanation:

Let t = 2

h = 122.5 - 4.9·2² = 122.5-19.6 = 102.9

Surface Area of cones
Instructions: Find the surface area of each figure. Round your answers to the nearest tenth, if necessary.

Answers

9514 1404 393

Answer:

  64.1 ft²

Step-by-step explanation:

The area of the cone is given by ...

  A = πr(r +h) . . . . for radius r and slant height h

  A = π(2 ft)(2 ft +8.2 ft) ≈ 64.1 ft²

What is the x-coordinate of the point of intersection for the two lines below?
-6 + 8y = -6
7x -10y = 9

Answer choices
1.) -6
2.) -3
3.) 3
4.) 7

Answers

Answer:

c.

Step-by-step explanation:

Solve the following formula for a.

Answers

Answer:

B is correct .trust me

Step-by-step explanation:

If a and b are positive numbers, find the maximum value of f(x) = x^a(2 − x)^b on the interval 0 ≤ x ≤ 2.

Answers

Answer:

The maximum value of f(x) occurs at:

[tex]\displaystyle x = \frac{2a}{a+b}[/tex]

And is given by:

[tex]\displaystyle f_{\text{max}}(x) = \left(\frac{2a}{a+b}\right)^a\left(\frac{2b}{a+b}\right)^b[/tex]

Step-by-step explanation:

Answer:

Step-by-step explanation:

We are given the function:

[tex]\displaystyle f(x) = x^a (2-x)^b \text{ where } a, b >0[/tex]

And we want to find the maximum value of f(x) on the interval [0, 2].

First, let's evaluate the endpoints of the interval:

[tex]\displaystyle f(0) = (0)^a(2-(0))^b = 0[/tex]

And:

[tex]\displaystyle f(2) = (2)^a(2-(2))^b = 0[/tex]

Recall that extrema occurs at a function's critical points. The critical points of a function at the points where its derivative is either zero or undefined. Thus, find the derivative of the function:

[tex]\displaystyle f'(x) = \frac{d}{dx} \left[ x^a\left(2-x\right)^b\right][/tex]

By the Product Rule:

[tex]\displaystyle \begin{aligned} f'(x) &= \frac{d}{dx}\left[x^a\right] (2-x)^b + x^a\frac{d}{dx}\left[(2-x)^b\right]\\ \\ &=\left(ax^{a-1}\right)\left(2-x\right)^b + x^a\left(b(2-x)^{b-1}\cdot -1\right) \\ \\ &= x^a\left(2-x\right)^b \left[\frac{a}{x} - \frac{b}{2-x}\right] \end{aligned}[/tex]

Set the derivative equal to zero and solve for x:

[tex]\displaystyle 0= x^a\left(2-x\right)^b \left[\frac{a}{x} - \frac{b}{2-x}\right][/tex]

By the Zero Product Property:

[tex]\displaystyle x^a (2-x)^b = 0\text{ or } \frac{a}{x} - \frac{b}{2-x} = 0[/tex]

The solutions to the first equation are x = 0 and x = 2.

First, for the second equation, note that it is undefined when x = 0 and x = 2.

To solve for x, we can multiply both sides by the denominators.

[tex]\displaystyle\left( \frac{a}{x} - \frac{b}{2-x} \right)\left((x(2-x)\right) = 0(x(2-x))[/tex]

Simplify:

[tex]\displaystyle a(2-x) - b(x) = 0[/tex]

And solve for x:

[tex]\displaystyle \begin{aligned} 2a-ax-bx &= 0 \\ 2a &= ax+bx \\ 2a&= x(a+b) \\ \frac{2a}{a+b} &= x \end{aligned}[/tex]

So, our critical points are:

[tex]\displaystyle x = 0 , 2 , \text{ and } \frac{2a}{a+b}[/tex]

We already know that f(0) = f(2) = 0.

For the third point, we can see that:

[tex]\displaystyle f\left(\frac{2a}{a+b}\right) = \left(\frac{2a}{a+b}\right)^a\left(2- \frac{2a}{a+b}\right)^b[/tex]

This can be simplified to:

[tex]\displaystyle f\left(\frac{2a}{a+b}\right) = \left(\frac{2a}{a+b}\right)^a\left(\frac{2b}{a+b}\right)^b[/tex]

Since a and b > 0, both factors must be positive. Thus, f(2a / (a + b)) > 0. So, this must be the maximum value.

To confirm that this is indeed a maximum, we can select values to test. Let a = 2 and b = 3. Then:

[tex]\displaystyle f'(x) = x^2(2-x)^3\left(\frac{2}{x} - \frac{3}{2-x}\right)[/tex]

The critical point will be at:

[tex]\displaystyle x= \frac{2(2)}{(2)+(3)} = \frac{4}{5}=0.8[/tex]

Testing x = 0.5 and x = 1 yields that:

[tex]\displaystyle f'(0.5) >0\text{ and } f'(1) <0[/tex]

Since the derivative is positive and then negative, we can conclude that the point is indeed a maximum.

Therefore, the maximum value of f(x) occurs at:

[tex]\displaystyle x = \frac{2a}{a+b}[/tex]

And is given by:

[tex]\displaystyle f_{\text{max}}(x) = \left(\frac{2a}{a+b}\right)^a\left(\frac{2b}{a+b}\right)^b[/tex]

what value of x is in the solution set of 8x-6>12+2x

Answers

Answer:

x>3

Step-by-step explanation:

8x - 2x > 12+ 6

-> 6x > 18

-> x > 3

[tex] \: \: \: \huge \rm{answer: \blue{ \boxed{ \rm{ \pink{x > 3}}}}}[/tex]

➖➖➖➖➖➖➖➖➖➖➖➖➖➖➖

[tex] \huge \blue{ \boxed{ \pink{\boxed{ \rm{ \blue{armed }\: account}}}}}[/tex]

➙[tex] \huge \rm8x-6>12+2x \\ \rm \huge8x-2x>12+6 \\ \huge\rm6x>18 \\ \huge \boxed{\rm{x>3}}[/tex]

➖➖➖➖➖➖➖➖➖➖➖➖➖➖

I hope you understood!✏

➖➖➖➖➖➖➖➖➖➖➖➖➖➖

Step-by-step explanation:

[tex] \huge \boxed{ \boxed{\rm{Hope \: this \: helps}}}[/tex]

Write the equation of the line that passes through the points (0, 4) and (- 4, - 5) . Put your answer in fully reduced slope intercept form , unless it is a vertical or horizontal line

Answers

Answer:

y=9/4x+4

Step-by-step explanation:

Start by finding the slope

m=(-5-4)/(-4-0)

m=-9/-4 = 9/4

next plug the slope and the point (-4,-5) into point slope formula

y-y1=m(x-x1)

y1=-5

x1= -4

m=9/4

y- -5 = 9/4(x - -4)

y+5=9/4(x+4)

Distribute 9/4 first

y+5=9/4x + 9

subtract 5 on both sides

y=9/4x+4

Five subtracted from seven times a number is 9. What is the number?

A) Translate the statement above into an equation that you can solve to answer this question. Do not solve it yet. Use
x
as your variable.

The equation is _____________


B) Solve your equation in part [A] for
Answer:
x=

Answers

Answer:

18

Step-by-step explanation:

7-5=2

2x9=18

7x2=14

14-5=9

9=7n-5

9=7n-5
9=7(2)-5
9=14-5
9=9

I could be wrong an misunderstood the entire thing, however I can reassure you 18 is not the answer as the question states “Five subtracted from seven times a number is 9”, therefore the final answer in part A) needs to equal 9.

y
Which point on the x-axis lies on the line that passes
through point C and is parallel to line AB?
5 4
C
NU
1
O (1,0)
O (1, 1)
0 (0, 2)
O (20)
А
54
214
2 3
4 5
х
h
B
3
4
ch

Answers

I think it's (2,0).

Because u use the slope of line AB to go down from point C until one of the answers are met.

The point on the x-axis that will make the line that passes through point C parallel to line AB is: D. (2, 0).

Slope of Parallel LinesTwo lines on a coordinate plane are parallel to each other if they have the same slope.Slope = change in y/change in x.

Slope of AB = -(3/6)

Slope of AB = -1/2

Slope of from point (2, 0) to point C(-2, 2):

Slope = (2 - 0)/(-2 - 2) = 2/-4

Slope = -1/2

Therefore, the point on the x-axis that will make the line that passes through point C parallel to line AB is: D. (2, 0).

Learn more about slope of parallel lines on:

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Triangle DEF has sides of length x, x+3, and x−1. What are all the possible types of DEF?

Answers

Triangle DEF is scalene

Must click thanks and mark brainliest

The triangle DEF will be a scalene triangle as all the sides of the triangle are unequal.

What is a scalene triangle?

A scalene triangle is a type of triangle which have all the sides to be unequal and similarly, all the angles will also be unequal to each other.

Given that:-

Triangle DEF has sides of length x, x+3, and x−1

it is given that all the sides of the triangle are x, x+3, and x−1 we can clearly see that for any value of x all the three sides will have different values. we can conclude from this that the triangle DEF is a scalene triangle.

Therefore triangle DEF will be a scalene triangle as all the sides of the triangle are unequal.

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What is the remainder when () = 3 − 11 − 10 is divided by x+3

Answers

Answer:

-18/x+3

Step-by-step explanation:

I need to know the answer please

Answers

Focusing on the center point of f(x) (0,0), we can see that it has moved to the left 4 units and up 3 units.

g(x) = [tex](\sqrt[3]{x + 4}) + 3[/tex]

Option C

Hope this helps!

If ‘BOXES’ is OBXSE, then BOARD is

Answers

9514 1404 393

Answer:

  OBADR

Step-by-step explanation:

The first two letters are swapped, and the last two letters are swapped.

  BOARD . . . becomes

  OBADR

Given the following matrices, what 3 elements make up the first column of the product matrix DA?

Answers

We have to figure out what the product of DA is,

[tex]\begin{bmatrix}-1&2&3\\8&-4&0\\6&7&1\\ \end{bmatrix}\begin{bmatrix}1\\3\\5\\ \end{bmatrix}=\begin{bmatrix}a\\b\\c\\ \end{bmatrix}[/tex]

We know that,

[tex]\begin{bmatrix}a&b&c\\d&e&f\\g&h&i\\\end{bmatrix}\begin{bmatrix}x\\y\\z\\\end{bmatrix}=\begin{bmatrix}ax+by+cz\\dx+ey+fz\\gx+hy+iz\\\end{bmatrix}[/tex]

So,

[tex]a=-1\cdot1+2\cdot3+3\cdot5=-1+6+15=20[/tex]

[tex]b=8\cdot1+(-4)\cdot3+0\cdot5=8-12=-4[/tex]

[tex]c=6\cdot1+7\cdot3+1\cdot5=6+21+5=32[/tex]

So the solution is,

[tex]a,b,c=\boxed{20,-4,32}[/tex]

Hope this helps :)

The least-squares regression equation
y = 8.5 + 69.5x can be used to predict the monthly cost for cell phone service with x phone lines. The list below shows the number of phone lines and the actual cost.

(1, $90)
(2, $150)
(3, $200)
(4, $295)
(5, $350)

Calculate the residuals for 2 and 5 phone lines, to the nearest cent.

The residual for 2 phone lines is $___


The residual for 5 phone lines is $___

Answers

Answer:

First one: 2.5

Second: -6

8.5+69.5(5) = 147.5

150 - 147.5 = 2.5

8.5 + 69.5(5) = 356

350 - 356 = -6

ED2021

The residual for 2 phone lines is $2.5.

The residual for 5 phone lines is -$6.

What is the residual in a least-square regression equation?

The residual is the vertical distance separating the observed point from your expected y-value, or more simply put, it is the difference between the actual y and the predicted y.

How to solve the question?

In the question, we are asked to find the residual for 2 and 5 lines using the least-squares regression equation y = 8.5 + 69.5x and the actual costs given to us.

We know that the residual is the vertical distance separating the observed point from your expected y-value, or more simply put, it is the difference between the actual y and the predicted y.

Thus for 2 phone lines:-

Actual Cost = $150.

Predicted Cost, y = 8.5 + 69.5*2 = 147.5.

Residual = Actual Cost - Predicted Cost = 150 - 147.5 = $2.5.

Thus, the residual for 2 phone lines is $2.5.

Thus for 5 phone lines:-

Actual Cost = $350.

Predicted Cost, y = 8.5 + 69.5*2 = 356.

Residual = Actual Cost - Predicted Cost = 350 - 356 = -$6.

Thus, the residual for 2 phone lines is -$6.

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find lub and glb of the following set E={0.2, 0.23, 0.234, 0.2343, 0.23434, 0.234343,.....}​

Answers

The lub is 0.23[tex]\mathbf{\overline{43}}[/tex], while the glb is 0.2

The given set is presented as follows;

E = {0.2, 0.23, 0.234, 0.2343, 0.23434, 0.234343,...}

The least upper bound, lub, of a set, E, is known as the supremum of the set which is the number B such that all x ∈ E are of the value x  ≤ B, while there all y ∈ E has a x ∈ E such that t < x

Therefore;

The supremum, lub of the given set is 0.23[tex]\overline{43}[/tex]

The greatest lower bound, glb, b, also known as the infimum, is defined as follows;

b is the greatest lower bound if for all xE then x ≥ b

Given that b < t, then where x ∈ E, there exist a x < t

The glb of the given set is 0.2

Learn more about lub, supremum, glb, infimum, here;

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I need help on this problem​

Answers

9514 1404 393

Answer:

  see attached

Step-by-step explanation:

(a) The graph is scaled by a factor of 2, and shifted up 1 unit. The scaling moves each point away from the x-axis by a factor of 2. The points on the x-axis stay there. The translation moves that scaled figure up 1 unit.

__

(b) The graph is reflected across the x-axis and shifted right 4 units. The point on the x-axis stays on the x-axis.

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