Finding a population Function

Question

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 $dP/dt = (b-d)P$.

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?

Answer 1

$dP/dt = (b-d)P$

To solve the equation put P on the LHS and dt on the RHS.

$\frac{1}{P}dP=(b-d)dt$

Now integrate:

$\int \frac{1}{P}dP=\int (b-d)dt$

$log(P)=(b-d)t+C$

Now solve the equation for P.

But without knowing the table I cannnot proof, which values the parameters b,d and C might have.