Hospital officials estimate that approximately N(p)=p^2+5p+900 people will seek treatment in an emergency room each year if the population of the community is 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?

Question

Hospital officials estimate that approximately N(p)=p^2+5p+900 people will seek treatment in an emergency room each year if the population of the community is  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?

anonymous · Answer

$$\frac{dN}{dt}=\frac{dN}{dp}\frac{dp}{dt}$$Take the derivative wrt p, evaluate for p=20, and multiply by 1.2 to get the increase in thousands.

anonymous · Answer

im confused im not sure how to do that...

anonymous · Answer

do dN/dp is the derivative of N(p) and what is dp/dt

anonymous · Answer

dp/dt is 1200 per year, or 1.2 thousand per year to make it fit with the units of the original function.

anonymous · Answer

The change in population with respect to time.

anonymous · Answer

but time is not given

anonymous · Answer

Sure it is.... "growing at the rate of 1,200 per year."