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A population researcher has found that the population P (in thousands) of a city in a particular year is a function of the number N (in thousands) of the jobs available in that year which is, in turn, a function of the economy E (in billions of dollars) of the state in which that city is located. The researcher has determined that for a particular year, E=204, dP/dN=8, and dN/dE=0.4.

Find dP/dE.

At E=204, the population increases by___________ thousand people for each billion dollar increase in the state's economy.

User NeoHQ
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Answer:

At E=204, the population increases by 3.2 thousand people for each billion dollar increase in the state's economy.

Explanation:

Given : A population researcher has found that the population P (in thousands) of a city in a particular year is a function of the number N (in thousands) of the jobs available in that year which is, in turn, a function of the economy E (in billions of dollars) of the state in which that city is located.

To find : The value of
(dP)/(dE) ?

Solution :

The researcher has determined that for a particular year,

E=204,
(dP)/(dN)=8, and
(dN)/(dE)=0.4.

Using chain rule,


(dP)/(dE)=(dP)/(dN)* (dN)/(dE)


(dP)/(dE)=8* 0.4


(dP)/(dE)=3.2

At E=204, the population increases by 3.2 thousand people for each billion dollar increase in the state's economy.

User TygerKrash
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