# logistic IVP

• Feb 12th 2009, 03:03 PM
razorfever
logistic IVP
logistic equation $\displaystyle \frac {dP}{dt} = rP \left( 1 - \frac PK \right)$

world population in 1990 was about 5.3 billion, with intrinsic growth rate r of 0.0038 per year, assume a carrying capacity K = 100 billion for the world population

how do i use that to write down the logistic IVP with t=0 in 1990???
• Feb 12th 2009, 03:41 PM
Jester
Quote:

Originally Posted by razorfever
logistic equation $\displaystyle \frac {dP}{dt} = rP \left( 1 - \frac PK \right)$

world population in 1990 was about 5.3 billion, with intrinsic growth rate r of 0.0038 per year, assume a carrying capacity K = 100 billion for the world population

how do i use that to write down the logistic IVP with t=0 in 1990???

This would be your initial condition $\displaystyle P(0) = 5.3$
• Feb 12th 2009, 03:55 PM
razorfever
do i then solve the following DE:

dP/dt = 0.0038P * (1 - (P/100))
and find the constant using P(0) = 5.3
and shouldn't P(0) equal 5300000000 or do i just multiply the final answer by 1 billion???
• Feb 13th 2009, 04:52 AM
Jester
Quote:

Originally Posted by razorfever
do i then solve the following DE:

dP/dt = 0.0038P * (1 - (P/100))
and find the constant using P(0) = 5.3
and shouldn't P(0) equal 5300000000 or do i just multiply the final answer by 1 billion???

Solve what you have. Use P(0)=5.3. The units of P are in billions.