Modeling Technology Adoption in a Community: Solving a Differential Equation

[aatkins09]

A new technology is introduced into a community of 5000 individuals. If the rate dN/dx at which the technology spreads through the community is JOINTLY PROPORTIONAL to the number of people who use the technology AND the number of people who do not use it,
(1)WRITE A DIFFERENTIAL EQUATION FOR THE NUMBER OF PEOPLE, N(x) WHO USE THE TECHNOLOGY.

(2)SOLVE FOR THE GENERAL SOLUTION TO THE DE BY ANY METHOD.

iF SOMEONE CAN HELP WITH THE EQUATION PART THEN I CAN SOLVE IT, I JUST HAVE NOOOOOO IDEA HOW TO GET THE EQUATION.

all I can think of is
dN/dx=N(x)
but there has to be more to it.

 

[tiny-tim]

welcome to pf!

hi aatkins09! welcome to pf!

A new technology is introduced into a community of 5000 individuals. If the rate dN/dx at which the technology spreads through the community is JOINTLY PROPORTIONAL to the number of people who use the technology AND the number of people who do not use it,
…
all I can think of is
dN/dx=N(x)
but there has to be more to it.

i don't see a "500" in there

it's really very simple, all you need to is to translate the english into maths

ok, try translating into maths:
i] "the number of people who use the technology"
ii] "the number of people who do not use it"

 

[HallsofIvy]

Do you understand what jointly proportional means?