Answer:
![N(t) = 972(1.015)^{t}](https://tex.z-dn.net/?f=N%28t%29%20%3D%20972%281.015%29%5E%7Bt%7D)
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:
![N(t) = N(0)(1+r)^{t}](https://tex.z-dn.net/?f=N%28t%29%20%3D%20N%280%29%281%2Br%29%5E%7Bt%7D)
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 ![N(0) = 972](https://tex.z-dn.net/?f=N%280%29%20%3D%20972)
Since then, the number of students has increased by 1.5% each year.
Increase, so r is positive. This means that ![r = 0.015](https://tex.z-dn.net/?f=r%20%3D%200.015)
Then
![N(t) = N(0)(1+r)^{t}](https://tex.z-dn.net/?f=N%28t%29%20%3D%20N%280%29%281%2Br%29%5E%7Bt%7D)
![N(t) = 972(1+0.015)^{t}](https://tex.z-dn.net/?f=N%28t%29%20%3D%20972%281%2B0.015%29%5E%7Bt%7D)
![N(t) = 972(1.015)^{t}](https://tex.z-dn.net/?f=N%28t%29%20%3D%20972%281.015%29%5E%7Bt%7D)
Growth function.
Find the number of students enrolled in 2014.
2014 is 2014-2002 = 12 years after 2002, so this is N(12).
![N(t) = 972(1.015)^{t}](https://tex.z-dn.net/?f=N%28t%29%20%3D%20972%281.015%29%5E%7Bt%7D)
![N(12) = 972(1.015)^{12}](https://tex.z-dn.net/?f=N%2812%29%20%3D%20972%281.015%29%5E%7B12%7D)
![N(12) = 1162](https://tex.z-dn.net/?f=N%2812%29%20%3D%201162)
The number of students enrolled in 2014 is 1162.