SOLUTION: The population density 'P' of a city depends on the radius chosen from the centre of the city. For a particular city, P= 10+40r-20r^2 where 'P' is measured in thousand and r is mea

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Question 870658: The population density 'P' of a city depends on the radius chosen from the centre of the city. For a particular city, P= 10+40r-20r^2 where 'P' is measured in thousand and r is measured in kilometers from the centre of the city.
a.) What is the population density at the centre of the city?
b.) What are the possible values of r? (Find the domain of values of r)
c.) Evaluate dP/dr.
d.) Find the value of r ( the distance from the centre of the city ) where the population density is greatest. Hence find the population density for this value of 'r'.
Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
a)P=10%2B40r-20r%5E2
P%280%29=10
10,000
b)r%3E=0
c)dP%2Fdr=40-40r
d) Max occurs where dP%2Fdr=0
40-40r=0
40=40r
r=1
P=10%2B40-20
P=30
30,000