Answer:
Explanation:
Given
In 2012
--- Birth rate
-- Death rate from '12 to '40
Solving (a): Equation for population from 2012
In 2012, we have the addition in population to be:
million
From 2012 to 2040, we have the death rate per year to be:
million/year
So, the differential equation is:
where t represents time
Express in millions
Solving (b): The solution to the equation in (a)
Make dP the subject
Integrate both sides
This gives:
Solve for c.
When t = 0; P = 7.02
So, we have:
So:
Solving (c): The population in 2050
We have:
In 2050, the value of t is:
So, the expression becomes