Question

Linear FunctionsWhen a new charter school opened in 1996, there were 410 students enrolled. Write a formulafor the function N(t), representing the number of students attending this charter school t yearsafter 1996, assuming that the student population:

Answer 1

Step-by-step explanation

So the school had 410 students in 1996. Assuming that every year t after 1996 the students population changes in s students per year (with s<0 when the population of students decreases and s>0 when it increases) then the number of students after t years is given by:

`N(t)=410+s\cdot t`

So in each of the cases mentioned by the question we just need to choose the correct value of s.

In the first case we have an increase of 20 students per year which implies s=20. Then we have:

`N(t)=20t+410`

In the second case we have a decrease of 48 students per year which means s=-48. Then we get:

`N(t)=410-48t`

In the third case we have an increase of 36 students but it's per 2 years. In order to write it as an increase per year we must divide it by 2: 36/2=18. Then we have s=18 and the equation is:

`N(t)=410+18t`

In the fourth case we have a decrease of 44 students every 4 years. Then in order to write it as a decrease per year we have to divide it by 4: 44/4=11. Therefore s=-11 and we get:

`N(t)=410-11t`

In the fifth case we are told that the number of students remains constant through the years. This is equal to an increase or decrease of 0 students per year which means that s=0 and the function is a constant:

`N(t)=410`Answer

Then the answers in order are:

N(t)=410+20t

N(t)=410-48t

N(t)=410+18t

N(t)=410-11t

N(t)=410