Question

question 7
linear functions
when a new charter school opened in 1999, there were 550 students enrolled. write a formula for the function $n(t)$, representing the number of students attending this charter school $t$ years after 1999, assuming that the student population:
increased by 40 students per year
$n(t) = $
decreased by 48 students per year
$n(t) = $
increased by 32 students every 2 years
$n(t) = $
decreased by 36 students every 4 years
$n(t) = $
remained constant (did not change)
$n(t) = $
increased by 5 students every semester (twice each year)
$n(t) = $

Explanation:

Step1: Define linear function form

A linear function has the form $N(t) = N_0 + mt$, where $N_0=550$ (initial students in 1999), $m$ is the annual rate of change, and $t$ is years after 1999.

Step2: Case1: +40 students/year

Annual rate $m=40$. Substitute values.
$N(t) = 550 + 40t$

Step3: Case2: -48 students/year

Annual rate $m=-48$. Substitute values.
$N(t) = 550 - 48t$

Step4: Case3: +32 students every 2 years

Annual rate $m=\frac{32}{2}=16$. Substitute values.
$N(t) = 550 + 16t$

Step5: Case4: -36 students every 4 years

Annual rate $m=\frac{-36}{4}=-9$. Substitute values.
$N(t) = 550 - 9t$

Step6: Case5: No change

Annual rate $m=0$. Substitute values.
$N(t) = 550 + 0t = 550$

Step7: Case6: +5 students twice/year

Annual rate $m=5\times2=10$. Substitute values.
$N(t) = 550 + 10t$

Answer:

1. $N(t) = 550 + 40t$
2. $N(t) = 550 - 48t$
3. $N(t) = 550 + 16t$
4. $N(t) = 550 - 9t$
5. $N(t) = 550$
6. $N(t) = 550 + 10t$