The equation you looking for would come out as 5*(x-8)^2 + 9
expand it out to get your standard form
Answer:
After about 22 years, the population of each community will be approximately 12400
Step-by-step explanation:
Given
![y_1 = 10000(1.01)^x](https://tex.z-dn.net/?f=y_1%20%3D%2010000%281.01%29%5Ex)
![y_2 = 8000(1.02)^x](https://tex.z-dn.net/?f=y_2%20%3D%208000%281.02%29%5Ex)
Required
The population of each community after certain years.
![(a)\ x = 12](https://tex.z-dn.net/?f=%28a%29%5C%20x%20%3D%2012)
We have:
![y_2 = 8000(1.02)^x](https://tex.z-dn.net/?f=y_2%20%3D%208000%281.02%29%5Ex)
![y_2 = 8000(1.02)^{12](https://tex.z-dn.net/?f=y_2%20%3D%208000%281.02%29%5E%7B12)
![y_2 = 10145.93](https://tex.z-dn.net/?f=y_2%20%3D%2010145.93)
![(b)\ x = 22](https://tex.z-dn.net/?f=%28b%29%5C%20x%20%3D%2022)
We have:
![y_2 = 8000(1.02)^{22](https://tex.z-dn.net/?f=y_2%20%3D%208000%281.02%29%5E%7B22)
![y_2 = 12367.83](https://tex.z-dn.net/?f=y_2%20%3D%2012367.83)
![(c)\ x = 16](https://tex.z-dn.net/?f=%28c%29%5C%20x%20%3D%2016)
We have:
![y_2 = 8000(1.02)^{16](https://tex.z-dn.net/?f=y_2%20%3D%208000%281.02%29%5E%7B16)
![y_2 = 10982.28](https://tex.z-dn.net/?f=y_2%20%3D%2010982.28)
![(d)\ x = 20](https://tex.z-dn.net/?f=%28d%29%5C%20x%20%3D%2020)
We have:
![y_2 = 8000(1.02)^{20](https://tex.z-dn.net/?f=y_2%20%3D%208000%281.02%29%5E%7B20)
![y_2 = 11887.60](https://tex.z-dn.net/?f=y_2%20%3D%2011887.60)