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Slowtown has a population of 3500 and is losing people at the rate of 150 per year.
Boomtown has a population of 1500 and is growing 5% per year.
In about how many years will the two towns have the same population?
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Slowtown population formula " after t years " is
s(t) = 3500 - 150t.
Boomtown population formula " after t years " is
b(t) = .
They want you determine the integer number of years t from the condition s(t) = b(t).
If you use equation
3500 - 150t = ,
then you will not be able to solve it algebraically: it can be solved only numerically,
using specialized software.
Another way is to calculate functions s(t) and b(t), using your calculator or software
like Excel spreadsheet.
It is the way which I used in my solution. It produced this table below
year Population Population
t s(t), Slowtown b(t), Boomtown
after t years after t years
(rounded to the closest integer value)
----------------------------------------------
0 3500 1500 <<<---=== starting numbers
1 3350 1575
2 3200 1654
3 3050 1736
4 2900 1823
5 2750 1914
6 2600 2010
7 2450 2111
8 2300 2216 (*)
9 2150 2327 (*)
10 2000 2443
From the table, you see that the populations will become equal
somewhen in the 9-th year (after 8 years, in the 9-th year). ANSWER
Solved.