Question

3. A city has a population of 23,000 in 2005, 27,600 in 2006, 33,120 in 2007, and 39,744 in 2008. If this pattern continues, what will be the population in 2012?
a. Write the iterative rule for the arithmetic or geometric sequence.
b. Answer the question and show all work.

Answer 1

The rule for this arithmetic sequence is  you multiply 1.2

Then you will keep multiplying 1.2 until you get to 2012 and you should get 82,413.1584 as your final answer!

Answer 2

a. It is a geometric sequence; the common ratio is 1.2. $a_{n}$ = $a_{1}$ * 1.2^n-1
b. We keep multiplying by 1.2 to 39744 until we reach 2012, in which case it is:
2009: 47692.8
2010: 57231.36
2011: 68677.632
2012: 82413.1584
Since people must be whole, we must round to the nearest whole number, which is 82413.
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Hope this helps!