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.
