Question

The town of Clueville has approximately 30 000 people. An arts major is researching
the spread of news across the town. She determines that 300 knew the news of Col.
Mustard's death the morning after it happened. After 1 day, she found that 900 people knew about the death. Solve the logistic equation
dy/dt = k*y( 1 - y/L),to estimate how many people in the town knew about the death after 4 days. Note: L is the total possible number of people who can know and k is the growth constant.

Answer 1

i think you need to integrate in this question.

Answer 2

every day the number of people who know triples

Answer 3

so you can use \(300\times 3^t\) where \(t\) is the number of days after the first day.
i have no idea what that other stuff is about, but whatever you get will be equivalent to \(300\times 3^t\)

Answer 4

since you are interested in after four days, we need no formula at all
day 0: 300
day 1: 900
day 2: 2700
day 3: 8100
day 4: whatever \(8100\times 3\) is

Answer 5

So what do I do with 300x3^t

Answer 6

u just calculate 3*8100, that would be your answer

Answer 7

what?

Answer 8

are you sure?

Answer 9

Its suppose to be a differential equation problem, I don't use DE's anywhere?

Answer 10

oh, i just followed satellite....
no, then u have to use diff. equation

Answer 11

How do I do it using differential equations. Can you take me through it?

Answer 12

use variable separable method,this is easily separable
bring dy and y terms on one side of = sign and dt term on other side,
what u get ?

Answer 13

dy/y(1 - y/2) = k*dt, is that right?

Answer 14

why L =2 ?
keep it as L.
otherwise its correct !

Answer 15

oh sorry!

Answer 16

Then I integrate?

Answer 17

What do I do with L?, its the total possible number of people that can know. What do I do with it in the integral

Answer 18

L is constant. it won't be a trouble while integration.
u need to integrate 1/y(1 - y/L)
u know how ,right ?

Answer 19

can you do it? cause I've been stuck on this forever. I'm making a mistake and I dont see it.

Answer 20

ok, u know partial fractions ?

Answer 21

not very well

Answer 22

write that as A/y + B / (1-y/L) = 1/y(1 - y/L)
find A and B

Answer 23

so u get
1/y - 1/ (y-L)

Answer 24

now integrate {1/y - 1/ (y-L)} dy

Answer 25

i think u can, that is easy

Answer 26

Sorry, I'm not getting it :/ I suck at partial fractions

Answer 27

integral y-29999ln(y-1)?