Respuesta :
Answer:
[tex]N(t) = 972(1.015)^{t}[/tex]
Growth function.
The number of students enrolled in 2014 is 1162.
Step-by-step explanation:
The number of students in the school in t years after 2002 can be modeled by the following function:
[tex]N(t) = N(0)(1+r)^{t}[/tex]
In which N(0) is the number of students in 2002 and r is the rate of change.
If 1+r>1, the function is a growth function.
If 1-r<1, the function is a decay function.
In 2002, there were 972 students enrolled at Oakview High School.
This means that [tex]N(0) = 972[/tex]
Since then, the number of students has increased by 1.5% each year.
Increase, so r is positive. This means that [tex]r = 0.015[/tex]
Then
[tex]N(t) = N(0)(1+r)^{t}[/tex]
[tex]N(t) = 972(1+0.015)^{t}[/tex]
[tex]N(t) = 972(1.015)^{t}[/tex]
Growth function.
Find the number of students enrolled in 2014.
2014 is 2014-2002 = 12 years after 2002, so this is N(12).
[tex]N(t) = 972(1.015)^{t}[/tex]
[tex]N(12) = 972(1.015)^{12}[/tex]
[tex]N(12) = 1162[/tex]
The number of students enrolled in 2014 is 1162.
