Re: separable and exact ODE

Re: separable and exact ODE

I'm sorry model A is P' = kP where P' is the first derivative.

Re: separable and exact ODE

Let *t* represent time measured in years and let July 1980 coincide with . Let represent the population at time *t* in billions. Using the given model, we have the IVP:

where

Separating the variables in the ODE, we have:

Integrate:

Now, you have two points on the curve, from which you may determine the two constants. Once you have these, then set to answer the question.

Re: separable and exact ODE

So I'm still a little lost. What is the k value? Is it the rate?

I found k = 5.055 - 4.473 = .582

where .582/7 = .0831 so that's the rate of the increase of people per year.

-plug k into the t equation to solve for c1 which gives me .2235

put c1 back into t equation and my answer is not correct. The answer is between mid 2020 and 2035 according to the book. Please show me where i'm going wrong.

Re: separable and exact ODE

We have the two points (0,4.473) and (7,5.055) so this gives us the system:

From the first equation, we find:

Putting this into the second equation, we find:

And so we have:

Now, let and we find:

This is the year 2026.

Re: separable and exact ODE

Cool I was thinking too hard. Thank you again!