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?

Answer 1

They give you an equation N(p) that represents the number of people who will week emergency treatment in terms of the population p in thousands. To find out the rate of increase in the number of people seeking treatment, you’ll need to take the first derivative of N(p). However, the population is also increasing in terms of time (let’s assign t = # of years) so you’ll need to take the derivative with respect to t.

Take the derivative of the N(p) equation with respect to t. Because p is in thousands, for a population 20,000 and growth rate 1,200 per year, p = 20 and dp/dt = 1.2. Plug these into the derivative and evaluate.