The student population at Oak Mountain High School for a given year can be modeled by the function

Question

�
(
�
)
=
550
(
1.12
)
�
P(t)=550(1.12)
t
, where t is the number of years since 1995.







Part A

How many students were there in 1995?

�
(
�
)
=
500
(
1.25
)
�
P(t)=500(1.25)
t




Part B

According to the function, the population is


by
% each year.



Part C

How many students can they expect in 2015? (Hint: Can you have a partial person? Round up)

Answer 1

The function given is P(t) = 550(1.12)^t.

Part A:
To find the number of students in 1995, we need to find the value of P(t) when t = 0 (since t represents the number of years since 1995).
P(0) = 550(1.12)^0 = 550(1) = 550
Therefore, there were 550 students in 1995.

Part B:
The population is increasing by a rate of 12% each year, as indicated by the growth factor (1.12) in the function.

Part C:
To find the number of students in 2015, we need to find the value of P(t) when t = 2015 - 1995 = 20.
P(20) = 550(1.12)^20 ≈ 1656.30
We need to round up, so we can expect approximately 1657 students in 2015.