Question

A high school had $1200$ students enrolled in $2003$ and $1500$ students in $2006$. If the student population $P$; grows as a linear function of time $t$, where $t$ is the number of years after $2003$.
$\left(a\right)$ How many students will be enrolled in the school in $2010$?
$\left(b\right)$ Find a linear function that relates the student population to the time $t$.

Answer 1

Given: Population is a linear function of $t$.

$\Rightarrow P=kt+C$, where $k$ and $C$ are constants.

In $2003$, given that $P=1200,t=0$

since $t$ is time in years from $2003$

$\Rightarrow 1200=k\left(0\right)+C\therefore C=1200$

In $2006$ $P=1500,t=2006-2003=3$

$\Rightarrow 1500=k\left(3\right)+1200\therefore k=100$

(A) In $2010$ $t=2010-2003=7$

$P=100\times 7+1200=1900$

(B) The linear function is $P=100t+1200$