Respuesta :
Answer:
At E=204, the population increases by 3.2 thousand people for each billion dollar increase in the state's economy.
Step-by-step 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 [tex]\frac{dP}{dE}[/tex] ?
Solution :
The researcher has determined that for a particular year,
E=204, [tex]\frac{dP}{dN}=8[/tex], and [tex]\frac{dN}{dE}=0.4[/tex].
Using chain rule,
[tex]\frac{dP}{dE}=\frac{dP}{dN}\times \frac{dN}{dE}[/tex]
[tex]\frac{dP}{dE}=8\times 0.4[/tex]
[tex]\frac{dP}{dE}=3.2[/tex]
At E=204, the population increases by 3.2 thousand people for each billion dollar increase in the state's economy.
