In this exercise, we estimate the rate at which the total personal income is rising in a metropolitan area. in 1999, the population of this area was 963,200, and the population was increasing at roughly 9300 people per year. the average annual income was $33,162 per capita, and this average was increasing at about $1300 per year (a little above the national average of about $1225 yearly). use the product rule and these figures to estimate the rate at which total personal income was rising in the area in 1999. (round your answer to three decimal places.)

4.923%

Step-by-step explanation:

Population in 1999

963,200

Average annual income

$33,162 per capita

Total personal income

963,200* 33,162 = $31,941,638,400

Population in 2000

963,200+9,300= 972,500

Average annual income

$33,162+ $1,300 =$34,462  per capita

Total personal income

972,500* 34,462 = $33,514,295,000

We must now find a number x such that  31,941,638,400 increased x% equals 33,514,295,000 . That is to say,

31,941,638,400*(1+x/100)= 33,514,295,000

Isolating x we have

x = 4.923%

And the rate at which total personal income was rising in the area in 1999 was 4.923%

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.