annual per-capita Internet usage modelled w/ logistic eqn

[preety]

Based on data from the U.S. Census Bureau, the annual per captia internet usage in the United States may be modeled by the differential equation:

dI/dt=0.002882I(232.2-I)

where I is the per capita internet usage in hours and t is the number of years since the end of 1995. A differential equation is an equation that contains a function and at least one of its derivatives. The U.S. Census Bureau also found that in 1999 the annual per capita internet usage was 90 hours.

A) The solution to this differential equation is I(t)=a logistic function. Find this logistic function.

B) Show that the logistic function you found satisfies the differential equation above.

C) Explain the real-world meaning of the constants in the differential equation above including their units.

D) Explain the significance of the horizontal asymptotes of your logistic function.

 

[stapel]

Based on data from the U.S. Census Bureau, the annual per captia internet usage in the United States may be modeled by the differential equation:

dI/dt=0.002882I(232.2-I)

where I is the per capita internet usage in hours and t is the number of years since the end of 1995. A differential equation is an equation that contains a function and at least one of its derivatives. The U.S. Census Bureau also found that in 1999 the annual per capita internet usage was 90 hours.

What are your thoughts? What have you tried? How far have you gotten? Where are you stuck?

Please be complete. Thank you!

Eliz.

 

[preety]

I don't know where to start from. I know the logistic equation. which is:
y=c/1+ae^-bx+k.

I don't know how to differentiate the equation to get it into a logistic function.

 

[DR._Glockman]

See attachment for direction field; dl/dt = .002882l(232.2-l), l(4) = 90

l(t) = 11619/[50+79e^(-1673001t/2500000 + 1673001/625000)]

Used Maple 8 to solve.

 

[preety]

How do I get a logistic equation from the following equation I was given. I don't understand what I am supposed to do at first. I already got the logistic equation. I just wanted to know what I am supposed to do for the very first step.

 

[Deleted member 4993]

Integrate the given function - to get your required function..

Show your work - tell us where you are stuck.

If you don't know how to integrate the given function - dust off your old calculus book and give it a review. You need to use 'partial fractions - and then the integrals would be 'ln' functions. If you have trouble with that - you are missing pre-req for this class.