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.

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 ?

Solution :

The researcher has determined that for a particular year,

E=204, , and .

Using chain rule,

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

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step-by-step explanation:

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step-by-step explanation:

12: 00 p.m. to 7: 00 p.m. is a total of 7 hours.

4: 00 p.m. to 7: 00 p.m. is a total of 3 hours.

this means that from 4: 00 p.m to 7: 00 p.m. this represents 3/7 of what was lost from 12: 00 p.m. to 7: 00 p.m.

after knowing this, after doing 11,600 - 6,800 = 4,800

4,800 represents 3/7 of what was lost for 7 hours.

we then divide 4,800 by 3 which gets 1,600.

because we know that 1,600 represents 1/7 of how much water was lost, we just have to multiply by 7, which gets 11,200.   after adding 11,200 to how much water was left at 7: 00 p.m. which was 6,800. 11,200 + 6,800 = 18,000

this means that the pool originally had 18,000 gallons in the pool.

you can also check your work by doing 18,000 - 4(1600), which becomes           1800 - 6400 which gets you 11,600.