Calculus 2: Definitions and modeling Please help solve 1-6. Please show your work.(Answer for number 6 is given at the bottom of the picture)

Identify each differential equation in #1-4 as ordinary or partial. Also indicate its order. (Not that it has any relevance to the question, but o(t) is called the Dirac delta function.) dy + 5y = 3e-5t dy 12 1. dt 3. dt y+ ty 1 du 2. day dy + 3y = 8(t - 4) 4. + r ar + 12 202 = 0 5. Verify that P(t) = Poet is the solution of the natural growth model dP dt =rP, P(0) = Po. (r and Po are constants.) 6. 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 #5 above, what would the predicted population be in 2000. (For comparison's sake, the actual population in 2000 was 249 million.) Selected Final Answer(s) 6. 2.4 billion