Can someone help with this equation?

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 t

sladkih [1.3K]

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)

$\frac{dy}{dt}\ \alpha\ y(1-y)$

$\frac{dy}{dt}=ky(1-y)$

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

b)

$\frac{dy}{dt}=ky(1-y)\\\frac{dy}{y(1-y)}=kdt\\\int\limits {\frac{dy}{y(1-y)}} \, =\int\limit {kdt}\\\int\limits {\frac{dy}{y}} +\int\limits {\frac{dy}{1-y}} =\int\limit {kdt}\\\\ln(y)-ln(1-y)=kt+c\\ln(\frac{y}{1-y}) =kt+c\\taking \ exponential \ of\ both \ sides\\\frac{y}{1-y} =e^{kt+c}\\\frac{y}{1-y} =e^{kt}e^c\\let\ A=e^c\\\frac{y}{1-y} =Ae^{kt}\\y=(1-y)Ae^{kt}\\y=\frac{Ae^{kt}}{1+Ae^{kt}} \\at \ t=0,y=10\%\\0.1=\frac{Ae^{k*0}}{1+Ae^{k*0}} \\0.1=\frac{A}{1+A} \\A=\frac{1}{9} \\$

$y=\frac{\frac{1}{9} e^{kt}}{1+\frac{1}{9} e^{kt}}\\y=\frac{1}{1+9e^{-kt}}$

At t = 2, y = 40% = 0.4

c) At y = 75% = 0.75

$y=\frac{1}{1+9e^{-0.8959t}}\\0.75=\frac{1}{1+9e^{-0.8959t}}\\t=3.68\ days$

5 0

2 years ago

a fox a coyote and a wolf weigh a total of 120 pounds the ratio of the weight of fox to the weight of coyote is 3:8 the weight o

ira [324]

There is not enough information to calculate this.

Knowing the weight ratio of the fox to coyote as 3:8 in no way allows you to know the respective ratio of the wolf. To know the weight of the wolf would require knowing its ratio value, then the weights of all 3 is an easy calculation. 
Example - 3:8:15 (f:c:w) is a plausible ratio based upon real-world weight averages for certain species/subspecies of the three. 
- knowing the values of the 3 terms as 3:8:15 gives a total of 3+8+15 = 26 ratio values 
- you then simply divide the total weight by this ratio value total; 120/26 = 4.62 
- so each ratio value is 4.62 units of weight*** 
- now, simply calculate the weight of each canid by multiplying its ratio value by the unit of weight... 
fox; 3 x 4.62 = 13.86 
coyote; 8 x 4.62 = 36.96 
wolf; 15 x 4.62 = 69.3 
Validate the ratios by adding the weights together (we should get 120) 13.86 + 36.96 + 69.3 = 120.12 
The total is slightly out because that 4.62 figure was a rounding up. 

Now, the thing is, there is nothing given that allows us to know exactly what ratio value the wolf should be, I chose 15 myself because that is a real-world plausible value when compared to 3:8 for the other 2. Changing it to 16, say, means that there are now 27 ratio values total giving a ratio value of 120/27 = 4.44 obviously changing the weights of all 3.

5 0

3 years ago

Please help 15 points bc I’m new and only have like 50. I’ll also give branliest

Veronika [31]

It’s 12

On the first side (smaller triangle/ ABC) the give you one side that equals 4 and on the next triangle (bigger triangle/ DEF) it’s 8 meaning you’re going to multiply each corresponding side by 2

6 0

1 year ago

Is this statement true or false?

Sloan [31]

Answer:

True

Step-by-step explanation:

A down payment is mostly for deposit reasons with insurance. It also let's the landlord know you will be moving in soon. They will use that money for repairs when you move out. You have a chance of getting it pack if they find no damages :D

3 0

3 years ago

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Of the following sets, which represents a function? Situation A = {student's name, all the colors that the student likes} Situat

luda_lava [24]

Answer:

Situation A

Step-by-step explanation:

please mark as brainlist answer

8 0

2 years ago

Read 2 more answers