(a) Using Equations (1.5.5) and (1.5.6), and the fact that r and C are positive, der...

(a) Using Equations (1.5.5) and (1.5.6), and the fact that r and C are positive, derive two inequalities that P₀, P₁, P₂ must satisfy in order for there to be a solution to the logistic equation satisfying the conditions

(b)The initial population in a town is 10,000. After 5 years this has grown to 12,000, and after 10 years to 18,000. Is there a solution to the logistic equation that fits this data?