in 2013, the number of people living in a small town was 284. it was estimated that the towns population would increase by 4%

The situation can be modeled by a geometric sequence with an initial term of 284. The student population will be 104% of the prior year, so the common ratio is 1.04.
Let
P
P be the student population and
n
n be the number of years after 2013. Using the explicit formula for a geometric sequence we get

P
n
=
2
8
4
⋅
1
.
0
4
n
P
​n
​​ =284⋅1.04
​n
​​
We can find the number of years since 2013 by subtracting.
2
0
2
0
−
2
0
1
3
=
7
2020−2013=7
We are looking for the population after 7 years. We can substitute 7 for
n
n to estimate the population in 2020.

P
7
=
2
8
4
⋅
1
.
0
4
7
≈
3
7
4
P
​7
​​ =284⋅1.04
​7
​​ ≈374
The student population will be about 374 in 2020.

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