when a new charter school opened in 1995, there were 240 students enrolled. write a formula for the equation…
when a new charter school opened in 1995, there were 240 students enrolled. write a formula for the equation n, representing the number of students attending this charter school t years after 1995, assuming that the student population: a) increased by 48 students per year: b) decreased by 20 students per year: c) increased by 32 students every 2 years: d) decreased by 28 students every 4 years: e) remained constant (did not change):
Answer
Explanation:
Step1: Recall linear - equation form
The general form of a linear equation for a quantity $N$ that changes over time $t$ is $N = N_0+mt$, where $N_0$ is the initial value and $m$ is the rate of change. Here $N_0 = 240$.
Step2: Case a: Rate of increase is 48 per year
The rate of change $m = 48$. So the formula is $N=240 + 48t$.
Step3: Case b: Rate of decrease is 20 per year
The rate of change $m=- 20$. So the formula is $N=240-20t$.
Step4: Case c: Rate of increase is 32 every 2 years
The rate of change per year $m=\frac{32}{2}=16$. So the formula is $N = 240+16t$.
Step5: Case d: Rate of decrease is 28 every 4 years
The rate of change per year $m=-\frac{28}{4}=-7$. So the formula is $N=240 - 7t$.
Step6: Case e: No change
The rate of change $m = 0$. So the formula is $N=240$.
Answer:
a) $N = 240+48t$ b) $N = 240 - 20t$ c) $N = 240+16t$ d) $N = 240-7t$ e) $N = 240$