Hospital officials estimate that approximately N(p) = p²+5p+900 people will seek treatment in the emer- gency 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?

Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter6: Vector Spaces
Section6.7: Applications
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18. Hospital officials estimate that approximately
N(p) = p2+5p+900 people will seek treatment in the emer-
gency 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?
19. Boyle's law states that when gas is compressed at constant
temperature, the pressure P of a given sample satisfies the
equation PV = C, where V is the volume of the sample and
C is a constant. Suppose that at a certain time the volume is
30 in.³, the pressure is 90 lb/in.², and the volume is increasing
at the rate of 10 in.³ /s. How fast is the pressure changing at
this instant? Is it increasing or decreasing?
3
Transcribed Image Text:18. Hospital officials estimate that approximately N(p) = p2+5p+900 people will seek treatment in the emer- gency 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? 19. Boyle's law states that when gas is compressed at constant temperature, the pressure P of a given sample satisfies the equation PV = C, where V is the volume of the sample and C is a constant. Suppose that at a certain time the volume is 30 in.³, the pressure is 90 lb/in.², and the volume is increasing at the rate of 10 in.³ /s. How fast is the pressure changing at this instant? Is it increasing or decreasing? 3
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