Finding increase in emergency room patients with rate measure.

Question

Hospital officials estimate that approximately 𝑁(𝑝)=𝑝²+5𝑝+900 people will seek treatment in an emergency room each year if the population of the community is 𝑝 thousand. The population is currently 20,000 and is growing at the rate of 1,200 per year. At what rate is the number of people seeking emergency room treatment increasing? How do I find dN/dt?

Answer 1

dN/dt = (2p + 5)dp/dt = (2·20 + 5)·1.2 = 54 people per year