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

the answer is 200

step-by-step explanation:

the way the question is worded, it seems to imply the $264 interest is simple interest, not compound interest.

the simple interest for 2 years is $264; the simple interest for 1 year is $132.

$132 interest on a $600 investment means an interest rate of (132/600)*100 = 22%.

the value of $200 at 22% interest compounded annually for three years is

200%281.22%29%5e3

the amount of interest is that value, minus the original $200.