Answer:
3:36 PM
Step-by-step explanation:
Let fraction (y) of the people that heard the rumor , the differential equation that is satisfied by the by y is,

Solving the differential equation,
![y(t) = \frac{y_{o}}{[y_{o} + (1 + y_{o})e^{-kt}]}](https://tex.z-dn.net/?f=y%28t%29%20%3D%20%5Cfrac%7By_%7Bo%7D%7D%7B%5By_%7Bo%7D%20%2B%20%281%20%2B%20y_%7Bo%7D%29e%5E%7B-kt%7D%5D%7D)
The total number of inhabitants of the town = 2000
The number of people that heard the rumor = 160
At 8 AM, let t = 0,

= 0.08
By noon, half of the town as heard the rumor.
Then,

Therefore,
![\frac{1}{2} = \frac{0.08}{[0.08 + (1 - 0.08)e^{-4k}]}](https://tex.z-dn.net/?f=%5Cfrac%7B1%7D%7B2%7D%20%3D%20%5Cfrac%7B0.08%7D%7B%5B0.08%20%2B%20%281%20-%200.08%29e%5E%7B-4k%7D%5D%7D)
![\frac{0.08}{[0.08 + 0.92e^{-4k}]} = \frac{1}{2}](https://tex.z-dn.net/?f=%5Cfrac%7B0.08%7D%7B%5B0.08%20%2B%200.92e%5E%7B-4k%7D%5D%7D%20%3D%20%5Cfrac%7B1%7D%7B2%7D)




k ≈ 0.06106
Calculating time, t when y(t) = 90%
⇒ y(t) = 0.9
![\frac{0.08}{[0.08 + 0.92e^{-0.06106t}]} =0.9](https://tex.z-dn.net/?f=%5Cfrac%7B0.08%7D%7B%5B0.08%20%2B%200.92e%5E%7B-0.06106t%7D%5D%7D%20%3D0.9)





t = 7.59 hours
⇒ 7 hours 36 minutes
From 8 A.M. plus 7 hours 36 minutes = 3:36 PM
At 3:36 PM will 90% of the population have heard the rumor
Answer:
X/4 = 2
X=8
8 divided by 4 is 2 and 4x2 is 8
-2.5(1-2n)-1.5n
=-2.5+5n-1.5n
=-2.5+3.5n
Answer: B. -2.5+3.5n
Answer:
Amount of pets
Step-by-step explanation:
The price of a ticket doesn't necesarilly effect the amount of pets but the amount of pets effects the ticket price. Therefore, the ticket price needs the pets which means that is the independent variable and the number of pets is the independent.