Worlds population in 1960 was approximately 3 billion; in 2000 it was approximately 6 billion. Model this using a differential equation of your choice. You should include your reasons for your choice of models, the solution to the equation, and a graph spanning the given data and some time into the future.
Please help me get this finished!!! Medal when done! :)

Question

Worlds population in 1960 was approximately 3 billion; in 2000 it was approximately 6 billion. Model this using a differential equation of your choice. You should include your reasons for your choice of models, the solution to the equation, and a graph spanning the given data and some time into the future.
Please help me get this finished!!! Medal when done! :)

anonymous · Answer

Population growth is usually modeled so that future population growth rate depends linearly on the current size, $\frac{dP}{dt}=kP$ for some constant $k$ where $P$ is the population (say, in millions). a function of $t$, say, the time in years since 1960... we're given boundary conditions, particularly $P(0)=3$ and \(P(40)=6\.)

anonymous · Answer

Okay so when I write this equation out p(0)=3 and P(40)=3/20?

tkhunny · Answer

??  Why did the population shrink?

$\dfrac{dP}{dt} = kP$

This is separable.  Solve the differential equation, then worry about the known values.

anonymous · Answer

It didn't shrink...It went from 3 billion to 6 billion.

tkhunny · Answer

Not if p(0) = 3 and p(40) = 3/20 -- Where did '6' go?