Finding a population Function. I have been given the population of the USA from 1790 - 1980 (increasing in intervals of 10) and I am asked to solve this differential equation.

Uroskopieulm 2022-11-20 Answered
Finding a population Function
I have been given the population of the USA from 1790 - 1980 (increasing in intervals of 10) and I am asked to solve this differential equation.
Using t as time in years, and P as size of population at any time t.
It shows d P / d t = ( b d ) P.
I assume b and d are birth and death rates per 1000.
I have subbed in B d = 13 8.
I'm kinda puzzled I don't know what to do. I have made a table and graph on Excel with the data but I'm clueless. Any ideas guys and gals?
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Answers (1)

Kaeden Lara
Answered 2022-11-21 Author has 23 answers
Step 1
d P / d t = ( b d ) P
To solve the equation put P on the LHS and dt on the RHS.
1 P d P = ( b d ) d t
Now integrate:
1 P d P = ( b d ) d t
l o g ( P ) = ( b d ) t + C
Step 2
Now solve the equation for P.
But without knowing the table I cannnot proof, which values the parameters b,d and C might have.
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