Dear Sir
I would be grateful if you can help me to solve the the below questions
The answers are: a)31.54 million b) 13.44 million c)1179 million
thanks
Kingsman
Dear Adrian C. Keister
Thanks for the response and below is my working but I fail to find out where is my mistake; i just cannot get the answer.
Please help!
thanks
a) db/dt=0.0428b with when t=o,b=0
b) db/dt=-0.0167b with t=o b=o
c) db/dt=(0.0428-0.0167)b with when t=0.b=598100000
Kingsman
As I said, you should write your DE with population as the dependent variable, not births or deaths. The reason is that population will reflect both births and deaths, whereas births or deaths by themselves will not reflect the other. Here is my thought on the DE:
$\displaystyle \displaystyle \frac{dP}{dt}=0.0428P-0.0167P=0.0261P,$ subject to $\displaystyle P(0)=5.981\times 10^{8}.$ Here we have assumed that $\displaystyle t=0$ corresponds to the year 1974.
Now, what is the solution of this DE?
The issue is that both the birth rate and the death rate depend on the current population, according to the problem statement. And, of course, the population depends on the birth rate and the death rate. Therefore, in order to answer all your questions, you're simply going to have to find the population (the linking variable here) for all time, and then you can multiply by the indicated percentages to find the birth rate and the death rate in the indicated years.
Does that make more sense?
Dear Adrian C. Keister,
Thanks very much but I only manage to get the answer to part c leaving part b and a hanging in the
air without knowing where did I go wrong.I would appreciate very much if someone can show me the DE for part a and b
Thanks very much
Kingsman