Please tell me how to solve natural growth model and logistic growth mode

1) Verify that P(t) = P₀e^rt is the solution of the natural growth model

dtdP=rP,P(0)=P0.

(r and P₀ are constants)

(A) In 1790(t=0), the US population was 3.9 million;

In 1800(t=10), it was 5.3 million.

If the US population followed the model of the IVP in (1) above, what would the predicted population be in 2000.

2) Verify that P(t)=1+CertK, whereC=P0KP0 , is the solution of the logistic growth model

dtdP=r(1KP)P,P(0)=P0

(r, P₀, and K are constants)

(B) Assuming a carrying capacity of K=500 million and that the US population satisfies the logistic growth model on 2) above,

What is the predicted population for 2000? ( Using the same data points as in (A) )