Question

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.

Answer 1

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.