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**Use P0 = 3.9 (1790 population) as your initial condition to find the particular solution for this differential equation. Note: You may find it easier to solve in terms of the constants a and b. Show all the steps in your solution.**

This is the last step to a multi-part problem. I basically did a scatter plot of the relative growth rate by dividing an approximate growth rate by the US population between 1790 and 2000, did a linear regression and obtained the equation below.

This is the last step to a multi-part problem. I basically did a scatter plot of the relative growth rate by dividing an approximate growth rate by the US population between 1790 and 2000, did a linear regression and obtained the equation below.

**y = -.0001x + .0338 and (1/P)(dP/dt) = ax + b**

**I do not exactly know what they are asking to be done. Do they want me to solve for P'(t)? If so, how does the 1/P on the left side of the equation effect the right side? Any help would be appreciated. Thanks.**