What is model A?
I'm unsure of how to set up the differential equation for this problem:
Given that the earth's population on July 1980 was 4,473,000,000 and that on July 1987 it was 5,055,000,000. Assuming that P satisfies model A. When would the earth's population reach 10 billion? Thanks to all in advance for your help!
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.
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.