From 2006 to 2010, the population of a town declined to 22,000. the population is expected to continue to decline at a rate of 2.8% each year. what will the population be in 2040? round to the nearest whole number. enter your answer in the box.

Assume that a certain population is P. If the population has decreased 2.8% at the end of one year, this means that the population now is

100%P-2.8%P=97.2%P. Thus a decrease of 2.8% can means a multiplication by 97.2%, which is 97.2/100=0.972.

So, assume the population in 2006 was P. Then the population in 2007 was 

0.972P. Similarly, we can see that the population in 2008 was 0.972(0.972P).

The population in 2009 the population was  0.972(0.972(0.972P)), which is .

Finally, in the end of 2010 the population was .

The decline of the population from 2006 to 2010 was 22,000. This means that 

. Factorizing P we have:

. We can calculate , thus

.

We saw that the population after the n'th year after 2006 was .

2040 is the (2040-2006)=34th year after 2006, so the population in 2040 will be 

                       .

(to calculate : 0.972_*_=*_=*_=*_=*_=, one *_= for each 2)

Thus, the population in 2040 was 0.378*204,842=77,430.

Hope this helps you out . It's alot to read though

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.

square root of 36/6 = 2.449489743

square root of 16/6 = 1.632993162

square root of 6 = 2.449489743

the answer is square root of 16/6 because the square root of 36/6 is the same answer as square root of 6 = 2.449489743