A rumor spreads through a small town. Let y(t) be the fraction of the population that has heard the rumor at time t and assume that the rate at which the rumor spreads is proportional to the product of the fraction y of the population that has heard the rumor and the fraction 1−y that has not yet heard the rumor. a. Write the differential equation satisfied by y in terms of proportionality k.
b. Find k (in units of day−1, assuming that 10% of the population knows the rumor at time t=0 and 40% knows it at time t=2 days.
c. Using the assumptions in part (b), determine when 75% of the population will know the rumor.
d. Plot the direction field for the differential equation and draw the curve that fits the solution y(0)=0.1 and y(0)=0.5.

Answers

Answer 1
Answer:

Answer:

The answer is shown below

Step-by-step explanation:

Let y(t) be the fraction of the population that has heard the rumor at time t and assume that the rate at which the rumor spreads is proportional to the product of the fraction y of the population that has heard the rumor and the fraction 1−y that has not yet heard the rumor.

a)

(dy)/(dt)\ \alpha\  y(1-y)

(dy)/(dt)=ky(1-y)

where k is the constant of proportionality, dy/dt =  rate at which the rumor spreads

b)

(dy)/(dt)=ky(1-y)\n(dy)/(y(1-y))=kdt\n\int\limits {(dy)/(y(1-y))} \, =\int\limit {kdt}\n\int\limits {(dy)/(y)} +\int\limits {(dy)/(1-y)}  =\int\limit {kdt}\n\nln(y)-ln(1-y)=kt+c\nln((y)/(1-y)) =kt+c\ntaking \ exponential \ of\ both \ sides\n(y)/(1-y) =e^(kt+c)\n(y)/(1-y) =e^(kt)e^c\nlet\ A=e^c\n(y)/(1-y) =Ae^(kt)\ny=(1-y)Ae^(kt)\ny=(Ae^(kt))/(1+Ae^(kt)) \nat \ t=0,y=10\%\n0.1=(Ae^(k*0))/(1+Ae^(k*0)) \n0.1=(A)/(1+A) \nA=(1)/(9) \n

y=((1)/(9) e^(kt))/(1+(1)/(9) e^(kt))\ny=(1)/(1+9e^(-kt))

At t = 2, y = 40% = 0.4

c) At y = 75% = 0.75

y=(1)/(1+9e^(-0.8959t))\n0.75=(1)/(1+9e^(-0.8959t))\nt=3.68\ days


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Nina made 8 withdrawals fromher bank account. If each
withdrawal was for $20, what
was the total change in her
bank account?

Answers

the total change in her bank account would be $160,

if you multiply 8x$20 you get $160

PLEASE HELPPPPPPPPPPPPPP. What is 313 expressed as a decimal? a. 0.230769¯¯¯¯¯¯¯¯¯¯
b. 0.230769¯¯¯¯
c. 0.230769¯¯¯¯¯¯¯
d. 0.230769

Answers

To express 3/13 as a decimal, we divide the the numerator by the denominator. This will give us:
3÷13
=0.23076923
simplifying the above we get:
0.230769...
thus the correct answer is a] a. 0.230769

Answer:

0.23076923

Step-by-step explanation:

I think the question was mistyped. The question seems to be what is 3/13 expressed as a decimal? To do that simply divide de numerator by the denominator and get the answer, which is 0.23076923. In this way, you transformed a fraction into a decimal.

Describe how the graph of y | x| -4 is like the graph of y= |x| and how it is different.

Answers

The graph y=|x|-4 is obtained from the graph y=|x| dy moving down 4 units the graph y=|x|  along the y-axis (see, if x=0, then for y=|x|, y=0 and for y=|x|-4, y=-4).

These two graphs have the same form.

Answer:

The graph of y=|x|-4 is the same as y=|x|.

Step-by-step explanation:

HELP!How do you derive the equation of a circle?
How do you identify the center and radius of a circle?
How do you define the radian measure of an angle?
How are arc length and area of a sector related to proportionality?

Answers

Answer:

How do you derive the equation of a circle?

you can reverse the circle formula

How do you identify the center and radius of a circle?

You can identify the center because it is the middle of the circle and the radius can be draw from the center to the round part.

How do you define the radian measure of an angle?

it is the ratio of the length of the arc the angle forms÷the radius of the circle

How are arc length and area of a sector related to proportionality?

sector x radian

area = (r^2 x)/2

arc length = r x

they are not propotional

because Area / arc length = r/2 , (it's not a constant)

High Hopes

Barrii

Olivia picked 482 apples from the orchard's largest apple tree. She divided the apples evenly into 4 baskets. How many apples are in each basket? How many are left over?

Answers

Answer:

120 with 4 left

Step-by-step explanation:

482 divided by 4 is 120.5. so you throw 120 apples in each basket and you have 2 left.

Final answer:

Olivia divided the 482 apples she picked from the orchard's largest apple tree evenly into 4 baskets. Each basket contains 120 apples and there are 2 apples left over.

Explanation:

Total apples picked = 482

To determine the number of apples in each basket, we need to divide the total number of apples picked by Olivia, which is 482, by the number of baskets, which is 4.

Using division, 482 divided by 4 equals 120 remainder 2. Therefore, each basket contains 120 apples and there are 2 apples left over.

Learn more about Division here:

brainly.com/question/34253396

#SPJ3

Complete the Ratio Table

Answers

3 beets= 1.5
4 beets= 2
6 beets= 3
i’m pretty sure it’s just half of what the quantity is sorry if i’m wrong